THE   OUTLINES   OF   PHYSICS 


THE 


OUTLINES  OF  PHYSICS  ' 


AN  ELEMENTARY  TEXT-BOOK 


BY 

EDWARD   L.    NICHOLS 

PROFESSOR  OF  PHYSICS  IN  CORNELL  UNIVERSITY 


THE    MACMILLAN   COMPANY 

LONDON:  MACMILLAN  &  CO.,  LTD. 

1897 

All  rights  reserved 


COPYRIGHT,  1897, 
BY  THE  MACMILLAN  COMPANY. 


J.  S.  Gushing  &  Co.  -  Berwick  &  Smith 
Norwood  Mass.  U.S.A. 


UHI7BKSITY 


PREFACE 

I  HAVE  attempted  in  this  book  to  outline  a  short 
course  in  physics  which  should  be  a  fair  equivalent  for 
the  year  of  advanced  mathematics  now  required  for 
entrance  to  many  colleges.  Such  a  course,  especially  if 
it  is  to  be  accepted  as  an  alternative  entrance  subject, 
should  possess  at  least  an  equally  great  disciplinary 
value. 

To  possess  this  disciplinary  value,  physics  must  be 
taught  by  laboratory  methods,  and  the  experiments  should 
be,  as  far  as  possible,  of  a  quantitative  nature.  The 
student  should  be  given  ample  practice  in  the  measure- 
ment of  length,  mass,  and  time;  and  he  should  be  taught 
how  to  arrange  and  interpret  his  results  and  how  to 
express  them  graphically  by  means  of  curves.  In  this 
way  only  can  the  science  be  adequately  taught,  and  the 
younger  the  student  the  more  imperative  is  the  adoption 
of  such  methods. 

In  this  book,  accordingly,  experimental  work  is  given 
a  prominent  place.  The  experiments  have  been  chosen 
with  a  view  to  the  illustration  of  the  leading  principles  of 
physics.  In  the  selection  of  the  methods  and  of  the 
apparatus  used,  I  have  always  had  in  view  the  greatest 


VI  PREFACE 

possible  directness  and  simplicity,  rather  than  the  highest 
degree  of  accuracy.  The  inexperience  and  the  immatu- 
rity of  the  reader,  and  the  necessarily  inadequate  equip- 
ment of  school  laboratories,  have  been  likewise  borne  in 
mind. 

In  spite  of  the  place  accorded  to  experimental  study, 
the  volume  is  not  to  be  regarded  simply  as  a  laboratory 
manual  of  physics.  It  is  intended  to  fill  the  place  of  a 
text-book  and  laboratory  guide  combined,  in  those  cases 
where  the  amount  of  time  allotted  to  the  study  of  physics 
does  not  make  it  advisable  to  use  both  a  text-book  and 
a  laboratory  manual. 

The  successful  use  of  such  a  book  implies  a  teacher  whose 
knowledge  of  physics  has  been  gained  through  practical 
work.  It  likewise  implies  the  existence  of  a  laboratory 
which,  although  it  may  be  homely  in  its  appointments, 
must  yet  contain  a  reasonable  amount  of  well-made  appa- 
ratus. The  list  of  instruments  essential  to  the  carrying 
on  of  an  effective  course  of  laboratory  practice  in  physics 
is  not  a  large  one.  It  includes  certain,  standard  appara- 
tus, such  as  the  balance,  the  air  pump,  the  thermometer, 
the  projecting  lantern,  the  electrical  machine,  and  the 
galvanometer ;  together  with  such  accessories  as  are  nec- 
essary to  the  use  of  these  instruments.  Without  such 
an  equipment  no  college  or  school  should  attempt  to  give 
instruction  in  physics. 

The  present  work  has  been  written  with  this  method  of 
teaching  in  view.  It  contains  statements  of  the  most 


PREFACE  vii 

important  principles,  and  descriptions  of  the  experiments 
to  be  performed  in  illustration  of  them.  I  have  endeav- 
ored to  make  these  descriptions  sufficiently  full  to  enable 
the  student  to  see  what  the  solution  of  each  problem 
demands  and  to  work  it  out  intelligently.  The  book 
has  purposely  been  shorn  of  all  but  the  briefest  men- 
tion of  the  countless  applications  of  physics  to  the  arts, 
with  the  details  of  which  too  many  of  our  modern  ele- 
mentary text-books  are  encumbered. 

To  my  wife,  who  made  the  drawings  for  nearly  all  the 
illustrations  in  this  volume,  I  desire  to  express  my  grati- 
tude. But  for  her  skillful  and  devoted  aid,  my  task 
would  have  been  a  much  more  difficult  one. 


E.   L.   N. 


PHYSICAL  LABORATORY  OF  CORNELL  UNIVERSITY, 
February  27,  1897. 


TABLE   OF   CONTENTS 
PART  I 

MECHANICS 

CHAPTER  PAGE 

I.  INTRODUCTION      .  ...."...         1 

II.  THE  LAWS  OF  MOTION        .......       10 

III.  THE  LAWS  or  FALLING  BODIES          .         .         .         .         .19 

IV.  GRAVITATION  IN  COMBINATION  WITH  OTHER  FORCES        .       31 
V.  THE  SIMPLE  PENDULUM 37 

VI.  THE  PHYSICAL  PENDULUM           .         .         .         .         .         .51 

VII.  KINETIC  ENERGY  ;  POTENTIAL  ENERGY  ;  WORK         .         .       58 

VIII.  MACHINES    .         .         .         ...         .                 -.         .       65 

IX.  THE  BALANCE     .         .         .         .         .         .         .         .         .75 

X.  COHESION,  ADHESION,  AND  FRICTION         ....       86 

XI.  ELASTICITY          .         ...?'-.         .         ....       95 

XII.  THE  PROPERTIES  OF  LIQUIDS      .         .         .         .         .         .     108 

XIII.  DENSITY       .         .         .         .  *      .         ....         .         .     122 

XIV.  PROPERTIES  OF  THE  SURFACE  FILM  OF  LIQUIDS       .         .     130 
XV.  PROPERTIES  OF  GASES        .         .         .        .                 .        .     137 

PART  II 

HEAT 

XVI.     NATURE  AND  EFFECTS  OF  HEAT        .....     148 
XVII.     CALORIMETRY 161 

XVIII.     PHENOMENA  ACCOMPANYING  FUSION  AND  LIQUEFACTION   .     174 

ix 


CONTENTS 

CHAPTER  PAGE 

XIX.     RELATIONS  BETWEEN  HEAT  AND  WORK  .         .         .     187 

XX.     TRANSMISSION  OF  HEAT  194 


PART  III 

ELECTRICITY  AND    MAGNETISM 

XXI.    INTRODUCTION  TO  ELECTROSTATICS        .         .         .         .211 
XXII.     CONDUCTORS  AND  NON-CONDUCTORS  ;  ELECTRICAL  MA- 
CHINES       .........     221 

XXIII.  DISTRIBUTION  or  THE  ELECTRIC  CHARGE  UPON  CON- 

DUCTORS     .........     235 

XXIV.  CONDENSERS 245 

XXV.     THE  ELECTRIC  SPARK 255 

XXVI.     THE  ELECTRIC  CURRENT 264 

XXVII.  THE  MAGNETIC  EFFECTS  OF  THE  CURRENT          .         .271 

XXVIII.     MAGNETISM .280 

XXIX.  THE    MEASUREMENT    OF    CURRENT,    ELECTROMOTIVE 

FORCE  AND  RESISTANCE 291 

XXX.  THE  HEATING  EFFECT  OF  THE  ELECTRIC  CURRENT    .     302 

XXXI.     ELECTROLYSIS 307 

XXXII.     THERMO-ELECTRICITY 315 

XXXIII.  ELECTROMAGNETIC  INDUCTION 321 

PART  IV 

SOUND 

XXXIV.  THE  PROPAGATION  OF  SOUND 334 

XXXV.     VIBRATING  BODIES  ;  PITCH  AND  TIMBRE      .         .         .341 

XXXVI.     EXPERIMENTS    WITH  TUNING  FORKS  ;  THE   MEASURE- 
MENT OF  PITCH  348 


CONTENTS  XI 

CHAPTER  PAGE 

XXXVII.     THE  VIBRATION  OF  STRINGS 355 

XXXVIII.     WIND  INSTRUMENTS  AND  RESONATORS  ....  362 


PART  V 

LIGHT 

XXXIX.     KEFLECTION  AND  REFRACTION      .        .         .         .        .  370 

XL.     DISPERSION 382 

XLI.     LENSES 390 

XLII.     POLARIZATION,  DOUBLE   REFRACTION  AND  INTERFER- 
ENCE ..........  403 

XLIII.       VISION  AND   THE    SENSE    OF   COLOR          ....  413 

APPENDICES 

I.     TABLE   OF  THE   RELATION  OF  BRITISH   MEASURES  TO  THE 

METRIC  SYSTEM         .         .   .  427 

II.     THE  USE  OF  CROSS-SECTION  PAPER      .         .        .        .        .  428 

III.  BALANCES  AND  WEIGHTS       .         .         .         .  .,...-        .         .  429 

IV.  READING  MICROSCOPES 432 

V.     FILTERING  PUMPS  .........  434 

VI.     THE  CONSTRUCTION  OF  A  SENSITIVE  GALVANOMETER  .         .  435 

VII.     A  SIMPLE  FORM  OF  GLASS  CELL          .....  439 

VIII.     THE  CONSTRUCTION  OF  AN  ELECTROSCOPE    ....  440 

IX.     THE  USE  OF  THE  LANTERN  .  441 


THE  OUTLINES  OF  PHYSICS 


PART   I  — MECHANICS 


CHAPTER   I 
INTRODUCTION 

1.  Physics  Defined.  —  Physics  deals  with  the  properties 
of  matter,  and  with  the  various  changes  and  motions  which 
matter  undergoes.     All  phenomena  due  to  the  presence  of 
life,  however,  are  generally  excluded  from  the  domain  of 
physics.     There  are  several  branches  of  physics  which  are 
so  distinct  and  so  important  that  they  are  generally  treated 
as  separate  sciences.     Such  are: 

Astronomy,  the  physics  of  the  outer  universe. 
Geology,  the  physics  of  the  crust  of  the  earth. 
Meteorology,  the  physics  of  weather  and  climate. 
Chemistry,  the  physics  of  the  atom. 

2.  Physical  Measurements.  —  In  ascertaining  the   prop- 
erties of  matter  and  studying  its  behavior,  the  student  of 
physics  must  make  measurements  of  three  kinds: 

(1)  Measurements  of  length. 

(2)  Measurements  of  mass. 

(3)  Measurements  of  time. 

3.  The  Metric  System.  —  It  is  of  the  greatest  convenience 
to  have  some  uniform  system  of  measures  in  which  the 

B  1 


THE  OUTLINES   OF  PHYSICS 


various  quantities  are  related  to  each  other  in  the  simplest 
possible  manner.  The  metric  system,  which  fulfills  these 
requirements  more  nearly  than  any  other,  has  been  adopted 
all  over  the  world  for  use  in  scientific  work. 

4.  The  unit  of  length  in  physical  measurements  is  the 
centimeter  (cm.).  What  a  centimeter  is,  expressed  in 
familiar  terms,  will  be  seen  from  Fig.  1,  in  which  inches 
and  centimeters  are  shown  side  by  side. 


lOths 

o         i 


CENTIMETERS 
4  5 


leths 


FNCHES 

FIG.  1, 


The  centimeter,  precisely  defined,  is  one  hundredth  part 
of  the  distance  between  two  parallel  transverse  lines  ruled 
upon  a  bar  of  platinum,  which  is  carefully  preserved  in 
the  Archives  of  Paris.  It  was  the  intention  in  construct- 
ing this  standard  to  have  the  distance  (a  meter)  precisely 
one  ten-millionth  of  the  distance  from  the  equator  of  the 
earth  to  the  north  pole  measured  along  a  meridian.  It 
was  soon  found  that  the  meter  did  not  correspond  very 
exactly  to  the  intended  length;  but  it  was  deemed  much 
more  satisfactory  to  use  the  bar  as  a  standard,  since  it 
could  be  accurately  copied,  than  to  retain  a  standard  of 


INTRODUCTION  3 

reference  which  could  never  be  directly  measured,  and  the 
precise  length  of  which  would  always  remain  in  dispute. 

5.  The  unit  of  mass  is  the  gram.  It  is  one  thousandth 
of  the  mass  of  a  piece  of  platinum  which  is  preserved  in 
the  Archives  in  Paris.  This  piece  of  metal,  which  is  called 
the  standard  kilogram,  was  given  as  nearly  as  possible  the 
same  mass  as  that  of  one  thousand  cubic  centimeters  of 
pure  water  at  4°  of  the  centigrade  scale.  The  gram  cor- 
responds therefore,  very  nearly  indeed,  to  the  mass  of  one 
cubic  centimeter  of  water  at  that  temperature. 

Water  is  chosen  for  the  purpose  of  this  definition  instead 
of  a  metal  such  as  platinum  or  gold  or  any  solid  material, 
because  it  is  easily  obtained  in  a  state  of  purity,  and 
because  the  mass  of  a  given  volume  at  a  given  temperature 
is  always  precisely  the  same.  The  density  of  a  solid,  how- 
ever, depends  upon  its  physical  structure  and  the  process 
by  which  it  is  prepared.  A  given  volume  of  any  metal 
does  not  therefore  always  possess  the  same  mass. 

A  cubic  centimeter  of  water  would  be  a  very  incon- 
venient standard  to  handle  in  the  actual  comparison  of 
masses.  Platinum  weights  were  therefore  prepared,  and 
these  were  adjusted  until  they  corresponded  in  mass  to 
the  definition.  These  constitute  the  actual  comparison 
standards. 

Figure  2  shows  a  gram  weight  in  brass,  the  true  size ; 
also,  for  comparison,  a  kilogram  of  the  same  material. 

The  precise  relation  of  the  centimeter  and  of  the  other 
units  of  the  metric  system  to  each  other  and  to  the  British 
units,  which  are  still  largely  used  in  the  operations  of  every- 
day life,  may  be  found  in  the  tables  of  Appendix  I.  The 
names  of  the  more  important  units  of  the  metric  system, 


THE  OUTLINES   OF  PHYSICS 


millimeter  (mm.),  centimeter  (cm.),  meter  (m.),  kilometer  (km.)  ; 
milligram  (mg.),  centigram  (eg.),  decigram  (dg.),  gram  (g.),  kilo- 
gram (kg.)  ;   liter  (1.)  ; 


A  KILOGRAM  OF  BRASS. 


FIG.  2. 

also  their  relations  to  one  another,  should  be  committed  to 
memory. 

The  following  approximate  relations  to  the  units  of  other 
systems,  which  can  also  readily  be  memorized,  are  very 
useful : 

Two  and  a  half  centimeters  make  an  inch  (nearly). 
A  meter  is  about  39T%  inches. 
A  kilometer  is  about  £  of  a  mile. 
A  gram  is  about  15T%  grains. 
A  kilogram  is  about  2T2^  pounds. 

A  liter  is  about  If  pints  (imperial)  or  rather  more  than  1  quart  (1-056) 
U.  S.  standard. 


INTRODUCTION 

6.  The  unit  of  time  is  the  second.  It  is  g^ 
mean  time  from  noon  to  noon.  The  instrument  by  which 
time  is  measured  is  the  clock,  which  is  a  machine  for  keep- 
ing a  pendulum  in  motion,  and  for  counting  its  vibrations. 
The  pendulum  is  of  such  a  length,  usually,  that  it  makes 
one  vibration  per  second  (see  further,  Chapters  V  and  VI). 

A  simple  apparatus  by  means  of  which  short  intervals  of 
time  are  indicated   to  the  ear,   but  not  counted,   is   the 


FIG.  3. 

metronome  (Fig.  3).  This  consists  of  a  short  pendulum 
driven  by  clockwork.  The  rate  of  the  pendulum  is  adjust- 
able by  means  of  the  sliding  weight  w,  between  40  vibra- 
tions and  208  vibrations  a  minute.  At  each  beat  it  ticks 
loudly.  The  metronome  is  used  chiefly  by  students  of 
music,  but  it  is  likewise  a  valuable  apparatus  in  the  physi- 
cal laboratory.  For  illustrations  of  its  application,  see 
Arts.  38,  40,  43,  44,  etc. 


6  THE  OUTLINES   OF  PHYSICS 

7.  Measurements  of  length  are  always  made  by  the  use, 
directly  or  indirectly,  of  a  divided  scale,  usually  a  copy, 
more  or  less  exact,  of  a  part  or  the  whole  or  some  multiple 
of  the  standard  meter. 

For  measurements  of  precision  the  divisions  of  the  scale 
are  ruled  with  a  diamond  upon  metal  or  glass,  giving  lines 
too  fine  for  use  with  the  naked  eye.  In  such  cases  observa- 
tions are  made  with  a  microscope. 

8.  The  Estimation  of  Tenths.  —  In  comparing  any  linear 
distance  with  a  scale,  the  boundaries  rarely  (one  may  say 
never)  coincide  precisely  with  the  scale  divisions.     The 
measurement,  therefore,  consists  of  two  operations. 

(1)  The  identification  of  the  two  divisions  lying  nearest 
to  the  boundaries  of  the  distance  to  be  measured. 

(2)  The  estimation  in  each  case  of  the  distances  between 
the  boundary  and  the  nearest  division.      Convenience  of 
notation  and  computation  make  it  desirable  that  the  esti- 
mate should  be  expressed  in  tenths,  and  the  second  opera- 
tion is  called  the  estimation  of  tenths. 

In  Fig.  4,  for  example,  ab  and  cd  are  lines  the  distance 
between  which  is  to  be  measured. 


FIG.  4. 

The  lines  3,  4,  and  65,  66,  are  neighboring  divisions  of 
a  scale,  by  means  of  which  the  measurement  is  to  be  made. 
The  observer  notes  that  ab  is  nearest  to  division  3,  and 
he  estimates  its  position  as  0-2  beyond  that  mark.  In  the 
same  way  the  position  of  cd  is  noted  as  65-3. 


INTRODUCTION  7 

These  observations  are  recorded  thus : 

Position  of  ab     3*2  scale  divisions 
Position  of  cd  65*3  scale  divisions 

Distance  ab~-cd  62-1  scale  divisions 

The  required  distance  is  thus  determined  to  within  0-1 
of  a  scale  division  (s.  d.). 

If  each  scale  division  is  a  tenth  of  one  centimeter 
(=  1  mm.),  a  very  common  case  because  that  is  the  small- 
est division  of  which  tenths  can  be  readily  estimated  by 
the  unaided  eye,  the  result  is  reduced  to  centimeters  by 
moving  the  decimal  point  one  place  to  the  left,  thus : 

62-1  s.  d.  =  6-21  cm.- 

The  estimation  of  tenths  is  an  operation  requiring  a 
certain  amount  of  practice.  It  affords  excellent  training 
for  the  eye,  and  is  an  essential  attainment  for  all  who  have 
occasion  to  use  the  decimally  divided  scales  which  are 
commonly  employed  in  science. 

The  necessary  practice  may  be  acquired  by  means  of  the 
following  experiment. 

9.    EXPERIMENT  1.  — The  Estimation  of  Tenths. 

Apparatus: 

(1)  A  scale  at  least  10  cm.  long  and  divided  to  millimeters. 

(2)  A  piece  of  cross-section  paper.     (See  Appendix  II.) 

Procedure  : 

(a)  Lay  the  scale  upon  the  paper,  its  lines  forming  an  oblique 
angle  with  those  of  the  latter.1 

!Note  that  the  estimation  of  tenths  of  the  smallest  parts  of  scales 
divided  into  eighths,  twelfths,  or  sixteenths,  does  not  in  the  least  facili- 
tate notation  or  computation  of  the  results.  It  is  on  account  of  the  use 
of  such  scales  in  everyday  life  that  most  persons  remain  unfamiliar  with 
so  simple  an  operation  as  the  estimation  of  tenths. 


8 


THE  OUTLINES   OF  PHYSICS 


(&)  Letter  every  tenth  line  of  those  which  lie  within  the  limits  of 
the  scale  a,  &,  c,  etc.,  from  left  to  right.     (See  Fig.  54.) 

(c)  Observe  the  position  of  the  lines  a,  b,  c,  etc.,  at  the  edge  of  the 
scale,  counting  to  the  nearest  division  to  the  left,  and  estimating 


FIG.  5. 

the  tenths  of  a  division.  Tabulate  the  observations  as  below,  and 
compute  from  them  the  most  probable  value  of  the  distance  between 
the  lines  upon  the  paper.  Taking  this  as  the  true  value,  compute  the 
positions  which  a,  6,  c,  etc.,  should  occupy  upon  the  scale,  and  thus 
determine  the  error  of  each  observation. 

Note  that  the  mean  value  of  an  interval,  computed  by  dividing  the 
sum  of  the  distances  from  a  by  the  sum  of  the  numbers  contained  in 
the  column  marked  "  number  of  intervals,  counting  from  a,"  is  slightly 
different  from  the  average  of  the  successive  differences.  The  former 
gives  a  more  probable  value,  because  it  gives  each  observation  due 
weight.  The  actual  size  of  the  error  in  reading  the  position  of  line  A, 
for  example,  is  not  likely  to  be  greater  than  in  reading  that  of  line  &. 
The  observed  distance  between  a  and  h  (90-6),  however,  is  that  of 
seven  intervals,  and  the  length  of  an  interval  computed  Jby  dividing 
that  distance  by  7,  gives  —  =  12-943.  In  the  same  way  ^  =  12-950, 

and  ?*?  =  12-920,  etc. 
6 


INTRODUCTION 
TABLE.  — ESTIMATION  OF  TENTHS. 


Error  of  read- 

ing (obtained  by 

Line. 

Scale  reading 
in  millimeters 
or    scale  divi- 

Distances 
from  line  "a" 
in  millimeters 
or  scale  divi- 

Number of 
intervals     in- 
cluded (count- 
ing from  line 

Successive 
differences. 

subtracting    each 
"distance      from 
a"  from  the  prod- 
uct of  the  "mean 
value  of  an  inter- 

sions. 

sions. 

"a"). 

nal  "     multiplied 

by    "  number    of 

intervals    includ- 

ed.") 

a 

1-2 

0-0 

b 

14-2 

13-0 

1 

13-0 

-  -061 

c 

27-1 

25-9 

2 

12-9 

+  -039 

d 

40-0 

38-8 

3 

12-9 

+  •039 

e 

52-9 

51-7 

4 

12-9 

+  -039 

f 

65-8 

64-6 

5 

12-9 

+  -039 

9 

78-9 

77-7 

6 

13-1 

-  -161 

h 

91-8 

90-6 

7 

12-9 

+  -039 

Sum  362-3 

28 

7190-6 

1  12  -943  =  Av.  interval. 

Mean  value  of  interval  = 


sum  of  distances  from  "a* 
sum  of  intervals  included 


362-3 

28 


=  12-939+ 


These  values  agree  among  themselves  and  with  the  mean  value  to 
within  two  digits  in  the  fourth  place,  whereas  the  values  of  the  in- 
terval obtained  by  considering  the  single  intervals  a  to  b,  b  to  c,  etc., 
separately  (see  column  of  successive  differences)  differ  among  them- 
selves by  two  in  the  third  place. 

The  example  illustrates  an  important  principle  in  the  computation 
of  the  results  of  physical  measurements. 


10  THE  OUTLINES   OF  PHYSICS 


CHAPTER   II 

THE  LAWS   OF  MOTION 

10.  The  fundamental  characteristics  of  motion  are  that  it 
occupies  time  and  that  it  takes  place  along  a  path.     The 
three  questions  to  be  answered  in  describing  a  motion  are : 

(1)  In  what  direction  ? 

(2)  How  fast? 

(3)  How  much  matter  is  there  in  the  moving  body  or 
system  of  bodies  ? 

Uniform  motion  is  motion  along  a  perfectly  straight  path 
and  with  unvarying  speed.  For  such  motion  the  answers 
to  the  three  questions  stated  above  would  afford  a  com- 
plete description. 

Uniform  motion,  however,  does  not  exist  in  nature, 
except  for  very  brief  intervals  of  time,  and  when  we  in- 
quire into  the  reasons,  we  find  that  it  is  because  neighbor- 
ing bodies  act  upon  the  moving  body,  tending  to  change 
its  motion  either  as  to  direction,  drawing  it  out  of  its 
straight  path,  or  as  to  speed.  Every  such  action  of  matter 
upon  matter  we  call  force. 

11.  The  Usual  Definition  of  Force.  —  Force  is   anything 
that   tends  to  produce  or  to   modify  motion.     Whenever  a 
force  exists,  investigation  shows  that  it  is  matter  which  is 
acting ;  one  or  more  'bodies  acting  upon  the  moving  body. 
There  are  no  exceptions  to  this  statement. 

Nothing  further  than  the  above  can  be  said  to  be  known 
about  the  nature  of  force ;  but  two  perfectly  definite  things 


THE  LAWS   OF  MOTION 


11 


can  always  be  stated  about  any  given  force,  the  existence 
of  which  is  observed : 

(1)  Its  direction. 

(2)  Its  size. 

12.  Graphical  Representation  of  Forces.  —  Any  force,  the 
point  of  application  of  which  is  known,  can  be  represented 
by  a  straight  line,  as  AB  (Fig.  6),  one  end  of  which  is  at 


FIG.  6. 


FIG.  7. 


the  point  of  application  A.  The  direction  of  the  line 
indicates  the  direction  in  which  the  force  acts,  its  length, 
the  size  of  the  force.  In  the  same  way  AB  and  AC 
(Fig.  7)  represent  two  forces  acting  upon  the  point  A. 

13.  The  Composition  and  Resolution  of  Forces.  —  Fre- 
quently a  number  of  forces  may  be  considered  as  acting 
upon  a  single  point.  In  such  cases  a  single  force  can 


FIG.  8. 


always  be  found  which  would  take  the  place  of  all  of 
them.  The  effect  of  this  force,  which  is  called  the  resul- 
tant, is  precisely  the  same  as  the  combined  effects  of  all 
the  original  forces  (or  components)  which  it  supplants. 


12 


THE  OUTLINES   OF  PHYSICS 


In  Fig.  8,  AB  and  A  O  are  forces  acting  upon  the  point 
A.     AR  is  their  resultant. 


14.  The  Parallelogram  of  Forces.  —  The  direction  of  the 
resultant  of  two  forces  and  its  size  may  be  found  by 
means  of  the  principle  of  the  parallelogram  of  forces; 
viz.: 

The  resultant  of  two  forces  which  act  upon  a  single  point 
is  found  ly  completing  the  parallelogram  of  which  the  forces 
in  question  form  adjacent  sides,  and  drawing  the  diagonal 
which  passes  through  the  point  of  application.  This  diago- 
nal represents,  both  as  to  size  and  direction,  the  resultant 
of  the  two  forces. 

EXAMPLE.  —  In  Fig.  8,  AB  and  AC  are  two  forces  act- 
ing upon  the  point  A.  They  form  adjacent  sides  of  a 
parallelogram  which  may  be  completed  by  drawing  BR 
parallel  to  AC,  and  OR  parallel  to  AB,  until  they  cut  one 
another  at  R.  If  A  and  R  be  joined,  we  shall  have  the 
diagonal  through  A,  and  this  line  represents  by  its  size 

and  direction  the  result- 
ant of  AB  and  AC. 


15.  Useful  Extensions 
of  the  Parallelogram  of 
Forces.  —  (1)  Any  num- 
ber  of  forces  acting  upon 
a  single  point  may  be 
combined,  and  their  re- 
sultant may  be  found  by 
taking  them  pairwise 
successively  until  only 
a  single  pair  remains. 


FIG.  9. 


THE  LAWS   OF  MOTION 


13 


The  resultant  of  this  pair  of  forces  will  be  the  resultant  of 
all  the  original  forces. 

EXAMPLE.  —  Let  AB,  AC,  AD,  AE  (Fig.  9),  be  forces. 
AB  and  AC  combined  furnish  the  resultant  ARl  (Fig.  9). 
AR1  may  now  be  combined  with  AD,  giving  a  resultant 
ARn,  and  this  in  turn  taken  with  AE,  gives  ARm,  which 
is  the  resultant  of  all  the  original  forces. 

(2)  The  only  lines  in  the  diagram  (Fig.  9)  which  are 
essential  to  the  construction  are  AB,  BR^  R1Rn,  72n72m. 

Instead  of  drawing  the  various  parallelograms  and  their 
diagonals,  we  may,  knowing  the  sizes  and  directions  of  the 
forces  AB,  AC,  AD, 
and  AE  (Fig.  9),  draw 
AB  as  in  Fig.  10,  then 
BR1  from  B  (hav- 
ing the  direction  and 
length  of  AC),  R^n 
from  R1  with  the  direc- 
tion arid  length  of  AD, 
and  72n72m  from  Rn 
with  the  direction  and  length  of  AE.  If  A  and  Rni  be 
then  joined,  a  polygon  will  be  formed  (called  the  polygon 
of  forces).  The  side  ARm  will  be  the  resultant  of  AB, 
A  C,  AD,  and  AE.  It  will  be  seen  that  ARm  is  identical 
with  the  corresponding  line  in  Fig.  9,  which  was  obtained 
by  means  of  the  parallelogram  of  forces. 

16.  Newton's  Laws  of  Motion. — Sir  Isaac  Newton  ex- 
pressed the  fundamental  facts  with  reference  to  motion  in 
the  form  of  three  laws,  as  follows : 

THE  FIRST  LAW.  —  A  body  maintains  its  condition, 
whether  of  rest  or  of  uniform  motion,  in  a  straight  line, 


FIG.  10. 


14  THE  OUTLINES   OF  PHYSICS 

excepting  as  it  is  compelled  by  the  action  of  forces  to  alter 
that  condition. 

This  law  is  sometimes  called  the  law  of  inertia.  It  de- 
scribes an  important  negative  property  of  matter :  its  com- 
plete passivity  or  freedom  from  tendency  to  change  its 
condition  as  regards  the  amount  or  direction  of  its  motion. 
It  indicates  further  that  all  changes  of  motion  must  be 
regarded  as  being  brought  about  by  the  action  of  forces 
from  without. 

Illustrations. —  (1)  Imagine  a  block  of  smooth  metal  or 
wood  sliding  on  a  plane  horizontal  surface  such  as  ice.  It 
moves  more  and  more  slowly,  and  finally  comes  to  rest. 
Newton's  law  tells  us  that  we  are  not  to  look  to  any  prop- 
erty of  the  block,  by  which  it  strives  or  tends  to  come  to 
rest,  but  to  forces  acting  from  without.  We  find  these 
forces  in  the  friction  between  the  surface  of  the  block  and 
that  of  the  ice,  and  in  the  resistance  of  the  atmosphere. 
The  first  of  these  would  commonly  be  much  the  more  im- 
portant cause  of  retardation.  If  we  polish  the  surfaces, 
thus  reducing  the  friction  more  and  more,  the  block  will 
move  further  and  further,  with  a  given  initial  motion, 
before  coming  to  rest.  If  this  process  could  be  carried  on 
indefinitely,  and  finally,  if  the  atmosphere  were  removed, 
the  block  would  move  on  indefinitely  without  coming  to 
rest.  The  motion  of  the  block  would  approach  uniformity 
as  the  opposing  forces ,  were  removed. 

(2)  Imagine  the  above  experiment  to  be  tried  in  a  wind 
blowing  in  the  direction  in  which  the  block  is  moving.  If 
we  reduce  the  friction,  we  reach  a  point  where  the  block 
will  travel  faster  and  faster  under  the  action  of  the  force 
due  to  the  wind.  To  produce  uniform  motion,  either  the 
friction  and  the  action  of  the  atmosphere  must  be  annihi- 


THE  LAWS   OF  MOTION  15 

lated  as  in  the  former  example,  or  these  must  be  adjusted 
so  as  to  balance  one  another. 

(3)  Imagine  the  experiment  to  be  tried  in  a  transverse 
wind.  The  block  will  then  suffer  both  retardation  and 
deviation  from  its  course.  The  forces  of  friction  and  of 
the  wind  cannot  be  balanced,  and  uniformity  of  motion  is 
approached  only  as  friction  and  the  action  of  the  atmos- 
phere are  annihilated. 

The  processes  imagined  in  these  three  illustrations  cannot 
be  rigorously  carried  out,  hence  the  statement  made  in 
Art.  10,  that  uniform  motion  does  not  exist  in  nature 
excepting  during  brief  intervals  of  time.  Experiments 
involving  the  first  law  will  be  found  in  subsequent  sections. 

17.  THE  SECOND  LAW.  —  Change  of  motion  is  always 
proportional  in  amount  to  the  applied  force  (or  to  the  result- 
ant of  the  applied  forces),  and  takes  place  in  the  direction 
in  which  the  force  acts. 

The  second  law  leads  us  to  consider  the  precise  meaning 
of  the  term,  amount  of  motion.  To  put  a  very  large  body 
and  a  small  one  into  motion,  such  that  they  travel  at  the 
same  speed,  requires  different  amounts  of  force.  In  point 
of  fact  the  force  in  each  case  will  be  proportional  to  the 
mass.  The  expression,  amount  of  motion,  as  used  in  the 
second  law,  takes  into  consideration  both  the  speed  and 
the  mass  of  the  moving  body.  It  is  measured  by  the 
product  of  the  two. 

18.  THE  THIRD  LAW.  —  Every   action  (of  a  force)  is 
accompanied  by  an  equal  and  opposite  reaction. 

This  law  is  really  a  very  important  statement  concern- 
ing the  nature  of  force,  viz.  that  it  always  consists  of  an 
interaction  between  two  bodies  or  masses  of  matter. 


16  THE  OUTLINES   OF  PHYSICS 

What  it  was  that  Newton  desired  to  express  may,  per- 
haps, be  most  readily  shown  by  means  of  a  number  of 
familiar  illustrations. 

19.  Illustrations.  —  (1)  Imagine   two  precisely  similar 
boats  each  containing  one  man.     The  masses  of  the  two, 
including  the  occupants,  are  the  same.     A  rope  connects 
the  two  boats.     If  this  is  drawn  in,  the  boats  will  approach 
each  other   by   equal   amounts,    whether   drawn   by  both 
men,  or  by  either  one  singly,  the  other  end  being  fastened. 
The  force  always  takes  the  form  of  a  strain,  drawing  the 
boats  equally. 

(2)  If  for  one  of  the  boats  a  vessel  of  large  size  be 
substituted,   there   will    still    be    a   mutual   approach   of 
the   boat   and   the   larger   vessel,   whatever    be   the   size 
of   the   latter ;   and  the  amount  of  motion  (taken  in  the 
sense  in  which  that  term  is  used  in  Art.  17)  imparted 
to  the  two  will  be  equal,  from  whatever  end  the  rope  be 
drawn  in. 

(3)  The  thrust  of  the  shaft  of  a  steamship  is  equally 
great  in  both  directions,  forwards  against  the  hull   and 
backwards   against   the   water.     The   forward   thrust,  by 
virtue  of  which  the  ship  is  driven  onwards,  must  be  suit- 
ably met  to  prevent  a  movement  of  the  shaft  itself  towards 
the  bow  of  the  vessel. 

20.  Reaction  of  a  Jet  of  Water.  —  Reaction  shows  itself 
where  the  medium  of  force-transmission  is  a  liquid  or  a 
gas,  exactly  as  in  the  cases  where  solid  matter  intervenes. 
The  reaction  of  water  jets  is  a  familiar  example.     It  may 
be  illustrated  in  the  following  simple  manner. 

A  rubber  tube  firmly  attached  to  the  water  faucet  leads 
to  a  forked  tube  T,  and  thence  by  means  of  two  flexible 


THE  LAWS  OF  MOTION 


17 


arms  to  a  glass  tube, 
as  shown  in  Fig.  11. 
When  the  water  is  turned 
on,  it  finds  exit  at  the 
opening  0  in  the  side  of 
the  glass  tube.  The  re- 
action of  the  issuing  jet 
thrusts  the  tube  forcibly 
backwards,  and  in  spite 
of  the  attractive  force  of 
the  earth  it  is  supported  in  the  position  shown  in  Fig.  12. 


FIG.  12. 


18 


THE  OUTLINES  OF  PHYSICS 


A  familiar  example  of  the  same  effect  is  the  water 

tourniquet  used  for  the 
sprinkling  of  lawns.  Similar 
apparatus  may  be  driven  by 
means  of  the  jets  from  a 
receiver  of  compressed  air. 
One  of  the  earliest  of  all 
heat  engines,  Hero's  engine 
(Fig.  13),  depended  upon  the 
reaction  of  steam  jets,  and 
FIG-  13.  one  of  the  most  successful 

of  modern  steam  engines,  the  steam  turbine,  is  based  upon 

the  same  principle. 


THE  LAWS  OF  FALLING  BODIES  19 


CHAPTER   III 

THE  LAWS  OF  FALLING  BODIES 

21.  Galileo's  Experiments.  —  The  direct  observation  of 
the  flight  of  bodies  falling  freely  through  space  is  difficult 
on  account  of  the  high  speeds  which  they  acquire  in  a 
short  interval  of  time. 

The  first  accurate  studies  of  this  subject  were  made  by 
the  Italian  physicist  Galileo  (1604),  who  made  use  of  the 
leaning  tower  at  Pisa  for  his  experiments.  This  building, 
a  picture  of  which  is  shown  in  Fig.  14,  is  admirably 
adapted  to  such  a  purpose.  It  consists  of  a  series  of  open 
galleries,  one  above  another,  reaching  a  total  height  of  55 
meters,  or  about  179  feet.  By  dropping  bodies,  differing 
in  mass  and  form  and  composed  of  various  materials,  from 
these  galleries  to  the  ground,  and  noting  the  time  taken 
in  falling,  Galileo  succeeded  in  ascertaining  the  following 
important  facts  with  reference  to  the  motions  of  matter 
falling  freely  through  space  under  the  attractive  force  of 
the  earth:  (1)  Large  bodies  and  small  require  precisely 
the  same  time  to  fall  from  a  given  height  to  the  ground. 
In  other  words,  the  time  of  fall  is  independent  of  the  mass. 
(2)  Bodies  made  of  different  substances,  as  iron,  copper, 
stone,  wood,  etc.,  fall  in  the  same  time.  In  other  words, 
the  time  of  fall  is  independent  of  the  material  of  ivhich  the 
falling  body  is  composed. 

To  this  second  statement  Galileo  found  many  apparent 
exceptions.  A  sheet  of  paper,  a  leaf,  or  a  feather,  for 


20 


THE  OUTLINES   OF  PHYSICS 


example,  would  fall  much  more  slowly  than  a  bullet.  He 
was  able  to  show,  however,  that  this  difference  was  due 
to  the  resistance  of  the  air.  By  gathering  bodies,  which 


FIG.  14. 


THE  LAWS   OF  FALLING  BODIES  21 

from  their  form  offered  a  large  surface  to  the  action  of  the 
atmosphere,  into  compact  pellets,  he  found  that  they  ap- 
proached the  denser  bodies  more  and  more  nearly  in  their 
rate  of  falling.  Heavy  metals  like  gold,  on  the  other 
hand,  when  beaten  into  foil,  fluttered  slowly  downwards. 

22.  Gravitation.  —  The  general  conclusion  to  be  drawn 
from  these  experiments  is  that  the  earth  exerts,  upon  each 
particle  of  matter  separately,  a  force  which  is  proportional 
to  the  mass  of  the  latter,  but  is  independent  of  the  material 
of  which  it  is  composed.     This  force  is  called  gravitation. 

23.  The  Guinea  and  Feather  Experiment,  —  At  the  time 
when  Galileo  made  his  investigations,  the  knowl- 
edge of  the  properties  of  the  atmosphere  was  very 
vague  and  incomplete.     No  instrument  for  the  pro- 
duction  of   a   vacuum   had   as   yet  been   devised. 
Nearly    half    a    century    later,    when    Otto    von 
Guericke   invented  the  air  pump  (Cologne,  about 
1650),  one   of  the  uses  to  which  the   new  appa- 
ratus  was   put   was   the   verification    of    Galileo's 
statement  that,  but  for  the  resistance  of  the  air,  all 
bodies  would  fall  to  the  earth  with  equal  rapidity. 

The  form  of  the  experiment,  which  has  come 
down  to  the  present  time  under  the  name  of  the 
guinea  and  feather  experiment,  is  as  follows : 

A  glass  tube  about  a  meter  and  a  half  in  length 
and  from  five  to  ten  centimeters  in  diameter  (Fig. 
15),  is  closed  at  the  ends  by  means  of  brass  caps. 
In  one  of  these  is  inserted  a  stopcock  threaded  to 
fit  the  pump. 

The  tube  contains  a  metal  coin  and  a  feather,  or  IG'  *  ' 
sometimes  some  disks  of  tissue  paper.  If  these  be  brought 
to  one  end  by  holding  the  tube  in  a  vertical  position,  and 


22 


THE  OUTLINES   OF  PHYSICS 


FIG.  16. 


then  be  made  to  fall  freely  the  length  of  the  tube,  by 
suddenly  turning  the  latter  end  for  end,  the  difference 
in  the  rate  of  falling  will  be  very  noticeable.  If  the  air 
be  exhausted  from  the  tube,  however,  and  the  observation 
be  then  repeated,  the  denser  and  lighter  bodies  will  fall 
with  equal  rapidity. 

24.   Method  of  the  Inclined  Plane.  —  To  determine  the 

precise  law  followed  by 
A  bodies  falling  freely  under 
the  action  of  a  constant 
force  like  gravitation,  Gal- 
ileo made  use  of  the  in- 
clined plane.  His  method 
depends  upon  the  follow- 
ing principle. 

Let  B  (Fig.   16)   be   a 
ball  resting  upon  an  inclined  plane  AD. 

BE  is  the  force  between  it  and  the  earth,  under  the 
A    action   of   which   it   would  fall  vertically 
downwards  were  it  not  partially  supported 
by  the  plane. 

Owing  to  the  presence  of  the  latter,  BE 
is  in  part  expended  in  producing  pressure. 
In  point  of  fact,  we  must  regard  that  force 
(see  Art.  12)  as  resolved  into  two  compo- 
nents :  BC  perpendicular  to  the  plane,  and 
CE  parallel  to  it.  The  former  of  these 
components  produces  pressure,  but  no 
motion ;  the  latter,  CE,  alone  urges  the 
D  ball  down  the  inclined  plane.  If  the  grade 

FlG'  lr'          or  pitch  of  the  plane  be  slight,  CE  will  be 
small  as  compared  with  the  original  force  BE,  and  the 


THE  LAWS   OF  FALLING  BODIES 


23 


ball  will  move  slowly,  but  will  follow  the  same  laws  of 
motion  as  though  it  were  falling  freely  under  the  action  of 
BE.  If  the  plane  becomes  horizontal,  CE  vanishes  and 
the  whole  of  BE  is  consumed  in  the  production  of  pres- 
sure. If  the  plane  be  very  steep,  as  in  Fig.  17,  CE 
approaches  BE  in  size,  and  the  pressure-producing  compo- 
nent, BO,  diminishes.  Finally,  if  the  plane  be  vertical, 
QE  equals  BE,  pressure  against  the  plane  ceases,  and  the 
ball  falls  freely  under  the  action  of  gravitation. 

25.    EXPERIMENT   2. —  Determination  of  the  Laws  of  Motion  by 
Means  of  the  Inclined  Plane. 

Apparatus : 

(1)  A  smooth  wooden  plane  not  less  than  4  m.  long.     (A.  stout 
board  or  plank  planed  011  one  side  will  do.) 

(2)  A  wooden  ball  about  10  cm.  in  diameter,  or  a  smaller  ball  of 
metal. 

(3)  A  metronome  set  to  beat  seconds. 


FIG.  18. 

Procedure  : 

(a)  Mount  the  plane  upon  two  tables  as  shown  in  Fig.  18.  It 
must  be  inclined  at  such  an  angle  that  the  ball  released  at  a,  without 
initial  impetus,  will  take  rather  more  than  three  seconds  to  reach  the 
lower  end.  Adjust  a  basket  or  other  receptacle  at  R  to  catch  the  ball 
at  the  end  of  its  trip.  Provide  three  uprights  or  markers,  capable  of 
being  fastened  firmly  to  the  edge  of  the  board  at  any  point,  yet  easily 
shifted.  Small  joiner's  clamps  (with  which  every  laboratory  and 


24  THE  OUTLINES   OF  PHYSICS 

physics  class-room  should  be  amply  supplied),  screwed  to  the  edge  of 
the  plank,  as  shown  in  the  diagram,  make  convenient  markers. 

(&)  Set  up  the  metronome  in  a  position  where  it  can  conveniently 
be  started  and  stopped. 

(c)  Having  set  the  metronome  in  motion,  hold  the  ball  opposite 
the  line  a,  near  the  upper  end  of  the  plane. 

(d)  Release  the  ball  with  the  hand,  precisely  at  the  stroke  of  the 
metronome,  taking  care  to  impart  no  initial  impulse  to  it. 

(e)  Note  the  position  of  the  ball   at  the  third  stroke  after  the 
release,  and  set  a  clamp  or  upright  to  mark  the  same.     Repeat  opera- 
tions (J)  and  (e),  readjusting  the  clamp  until  satisfied  that  further 
trials  will  not  materially  improve  the  result.      (Trials  in  which  the 
release  is  obviously  too  early  or  too  late  may  be  rejected.) 

(/)  Measure  the  distance  from  the  clamp,  the  position  of  which 
we  may  designate  as  d,  to  the  starting  point  (a).  Lay  off  from  a 
along  the  plane  a  distance  ab,  equal  to  ^  of  ad,  and  mark  it  by  means 
of  a  clamp;  also  from  a,  a  distance  ac  equal  to  £  of  ad,  to  be  marked 
by  a  similar  clamp. 

(</)  The  positions  (b)  and  (c),  in  case  the  previous  operations  have 
been  carefully  performed,  will  mark  the  passage  of  the  ball  at  the 
first  and  second  strokes  of  the  metronome.  Verify  the  law  by  releasing 
the  ball  several  times  and  noting  its  position  at  the  end  of  each  time 
interval. 

The  above  outline  gives  the  experiment  of  the  inclined  plane  in 
its  simplest  form.  It  admits  of  various  refinements,  of  which  the 
most  important  and  most  easily  arranged  is  the  automatic  release  of 
the  ball  at  the  stroke  of  the  time-marker.  Such  a  modification  of 
the  procedure  is  convenient  and  it  adds  to  the  accuracy  of  the  results ; 
but  it  is  not  essential  to  the  success  of  the  experiment. 

The  results  of  Experiment  2  may  be  most  readily  analyzed  by 
arranging  them  in  tabular  form  as  below. 

The  inspection  of  these  data  brings  out  at  once  the  following  im- 
portant features  of  the  motion  of  a  ball  starting  from  a  state  of  rest 
and  rolling  down  an  inclined  plane.  (Since,  as  has  been  pointed  out, 
the  law  is  the  same  in  the  case  of  a  body  falling  freely  through  space, 
the  conclusions  are  applicable  to  that  case  also.) 

The  relative  distances  apart  of  the  uprights  (column  4)  give  the 
distances  traversed  by  the  ball  in  successive  seconds. 

For  the  first  second  the  previous  speed  was  zero,  the  ball  having 


THE  LAWS   OF  FALLING  BODIES 


25 


been  at  rest.  It  would  have  remained  at  rest  but  for  the  action  of  the 
force  of  gravitation.  The  whole  distance  (a  to  b)  is  therefore  due  sim- 
ply to  the  action  of  the  force  during  the  first  second. 

EXPERIMENT  2. 


1 

2 

3 

4 

5 

Relative 

Relative 

Marks. 

Distance  from  (a). 

Distances 

Distances 

Times. 

from  («). 

apart. 

a 

0-0  cm. 

0 

0  sec. 

(a  to  6)  d 

b 

4-4+  cm.  (calculated  and  verified) 

d 

1  " 

(b  toe)  3d 

c 

22-1-  cm.  (calculated  and  verified) 

4d 

2    " 

(ctod)  5d 

d 

397  cm.  (observed) 

Qd 

3   " 

The  distance  be,  traveled  in  the  second  time  interval,  is  made  up  of 
two  parts : 

(1)  The  distance  traversed  by  virtue  of  the  initial  speed  of  the  ball, 
at  the  beginning  of  the  interval. 

(2)  The  distance  traversed  in  consequence  of  the  action  of  the  force. 
The  whole  distance  be  is,  however,  3  d,  and,  since  the  distance  due  to 

the  continued  action  of  the  force  is  d  (as  in  the  first  second),  the  dis- 
tance ascribable  to  initial  speed  is  equal  to  2  d.  This  quantity  (2  rf) 
is  obviously  the  distance  which  the  ball,  if  cut  loose  from  all  further 
action  of  force  at  the  beginning  of  the  second,  would  travel  during 
that  second.  It  is  called  the  velocity  at  the  end  of  one  second. 

From  the  path  of  the  ball  during  the  third  time  interval,  i.e.  cd,  we 
may,  invthe  same  manner,  deduct  e?,  the  distance  due  to  the  continued 
action  of  the  force.  The  distance  4c?,  which  remains,  would  be  trav- 
ersed without  the  continued  action  of  the  force ;  it  is  the  velocity  at  the 
end  of  two  seconds. 

This  doubled  velocity  is  itself  traceable  to  two  sources : 

(1)  The  velocity  acquired  during  the  first  interval.     This  is  equal 
to2d. 

(2)  The  velocity  due  to  the  action  of  the  force  during  the  second 
interval.     This  is  evidently  equal  to  2  c?  also. 


26 


THE  OUTLINES   OF  PHYSICS 


The  velocity  which  a  force  is  capable  of  imparting,  in  consequence 
of  its  action  during  one  second,  affords  a  means  of  measuring  the 
force.  It  is  called  the  acceleration. 

The  measure  of  the  force  is  the  product  of  the  mass  of  the  body  acted 
upon  and  the  acceleration. 

The  Unit  of  Force  is  called  the  dyne.  It  is  the  force  which,  acting  for 
one  second  upon  a  gram  of  matter,  is  capable  of  producing  a  velocity 
of  one  centimeter  per  second. 

The  relations  with  which  we  have  had  to  do  in  this  discussion 
may  be  further  studied  by  means  of  Fig.  19. 

Conditions  of  the  Supposed  Motion.  —  A  force  /  equal  to  1  dyne, 
acting  upon  1  gram  of  matter  at  0.  (See  Fig.  20.) 

.0 


t=0 


=  i  sec. 


FIG.  20. 

Total  distance  traversed 
during  2d  second  =  3  d. 


t= 


Velocity  at  end  of  2d  sec- 
ond =  4  d. 

Total  distance  traversed 
during  3d  second  =  5  d. 


=  3  sec. 
>  f 

FIG.  19. 


Distance  traversed  in  one  second  under  ac- 
tion of  constant  force  =  d. 


Distance  traversed  on  account  of  previous 
action  of  force  for  one  second.  Affords  a 
measure  of  velocity  at  end  of  1st  second,  also 
of  acceleration  =  2  d. 


Additional  distance  traversed  owing  to  con- 
tinued action  of  force  during  2d  second  =  d. 


Distance  traversed  on  account  of  action  of 
force  during  1st  second  (or  in  other  words  on 
account  of  velocity  acquired  during  1st  sec- 
ond) =2  d. 


Distance  traversed  on  account  of  'action  of 
force  during  the  2d  second  (or  on  account  of 
velocity  acquired  during  2d  second)  =  2  d. 


Additional  distance  traversed  owing  to  con- 
tinued action  of  force  during  3d  second  =  d. 


THE  LAWS  OF  FALLING  BODIES  27 

We  have  thus  far  considered  only  the  three  seconds  of  time  covered 
by  Experiment  3.  Had  such  measurements  been  extended  over  a 
longer  interval,  it  would  have  been  found  that  the  ball  traversed  during 
the  4th  second  a  distance  equal  to  7  d.  Of  this,  2  d  is  ascribable  to  the 
acceleration  of  the  1st  second,  2  d  to  the  acceleration  of  the  2d  second, 
2  d  to  the  acceleration  of  the  3d  second,  while  1  d  is  due  to  the  con- 
tinued action  of  the  force  during  the  4th  second.  The  total  distance 
traversed  up  to  the  end  of  the  4th  second  would  be  16  d. 

During  the  5th  second  the  ball  would  have  traversed  a  distance  9  d 
made  up  in  the  same  manner,  and  so  on  indefinitely.  The  total  dis- 
tance traversed  during  the  five  seconds  would  be  25  d. 

26.  Conclusions  from  Experiment  2.  —  (1)  Comparing  col- 
umns 3  and  5  of  the  table,  we  see  that  the  distance 
traversed  is  proportional  to  the  square  of  the  time  occupied. 

This  relation  may  be  expressed  in  the  form  of  an  equa- 

tion, viz. 

s  =  dt2, 

in  which  s  is  the  total  distance  traversed  in  t  seconds,  and 
d  is  the  distance  traversed  during  the  first  second.  Or  in 
terms  of  the  acceleration  (a  = 


(2)  The  velocity  is  always  proportional   to   the   time 
spent  in  acquiring  it  and  to  the  force  acting.     Expressed 
in  the  form  of  an  equation,  the  relation  between  velocity 
(v),   time   (£),  and  acceleration   (a),  which  serves  as  a 
measure  of  the  force  and  is  of  course  proportional  to  it, 

is  as  follows  : 

v  =  at. 

(3)  The  acceleration  due  to  a  constant  force   is   con- 
stant.    It  may  be  found  by  dividing  the  velocity  at  any 
instant  by  the  time  required  to  produce  it. 

Acceleration  and  velocity  at  the  end  of  the  first  second  are 
therefore  represented  by  the  same  value,  viz.  2  d. 


28  THE  OUTLINES   OF  PHYSICS 

(4)  Force  acts  upon  moving  bodies  and  upon  bodies  at 
rest  alike  and  in  precisely  the  same  way.  This  is  the 
assumption  upon  which  the  experiment  is  based.  There  is 
every  evidence,  from  the  character  of  the  results,  that  the 
assumption  is  warranted.  Further  direct  evidence  of  its 
truth  will  be  found  later.  (See  Chapter  IV.) 

As  has  been  pointed  out  in  Arts.  16  and  17,  velocity  and 
acceleration,  like  force,  are  "directed  quantities."  They 
may  be  resolved  into  components,  or  compounded  to  find 
a  resultant,  like  forces,  by  the  use  of  the  principle  of  the 
parallelogram.  It  is  in  this  way  that  the  effect  of  a  given 
force  upon  a  body  already  in  motion  is  most  conveniently 
determined. 

27.  Acceleration  due  to  Gravitation.  —  This  important 
quantity  may  be  determined  in  a  number  of  ways. 

From  the  experiment  of  the  inclined  plane,  for  example, 
we  can  determine  the  acceleration  of  the  ball.  If  the  pitch 
of  the  plane  be  measured,  the  relation  of  the  component 
CE,  which  urges  the  ball  down  the  plane  (Fig.  18)  to  BE, 
which  represents  gravitation,  can  be  ascertained.  The 
acceleration  due  to  the  latter  will  bear  the  same  relation 
to  the  acceleration  of  the  ball  that  BE  bears  to  CE.  The 
result  will  be  only  a  rough  approximation  to  the  true  value, 
however,  unless  we  take  account  of  the  rotary  motion  of 
the  ball,  and  of  the  errors  due  to  the  resistance  of  the 
air.  The  true  value  of  the  acceleration  of  gravitation 
varies  between  978-1  cm.  at  the  earth's  equator  and 
983-4  cjn.  at  the  poles.  In  latitude  45°,  at  the  level  of 
the  sea,  it  is  980-6  cm.  (nearly).  For  the  values,  at 
various  places,  determined  with  the  utmost  precision,  see 
Art.  49. 

The  above  is  the  velocity  which  a  body  falling  freely 


THE  LAWS   OF  FALLING  BODIES 


29 


through  space  for  one  second  will  acquire.  The  distance 
which  the  body  will  fall  during  the  first  second  is  one  half 
the  acceleration,  or  about  490  cm. 

28.    EXPERIMENT  3.  —  Verification  of  the  Distance  of  Free  Fall. 

Apparatus  : 

(1)  A  hook  or  screw  eye  mounted  about  500  cm.  above  the  floor, 
viz.  in  the  edge  of  a  small  bracket  attached  to  the  wall  or  to  a  suita- 
ble support  (Fig.  21). 

(2)  An  electromagnet ;   also  a  key  and  battery  and  conducting 
wires.     A  flexible,  double  lamp  cord  is  to  be  preferred.     The  same 
should  be  about  600  cm.  in  length. 

(3)  A  strong  cord  fastened  to  the  yoke  of  the  electromagnet  and 
passing  through  the  screw  eye  in  the  upper  bracket.     The  other  end 
of  the  cord  should  be  attached  to  a  clamp  or  cleat  upon  the  edge  of 
a  conveniently  placed  table. 


FIG.  21. 


30  THE  OUTLINES   OF  PHYSICS 

(4)  The  metronome  described  in  Art.  6. 

(5)  A  cast-iron  weight.     (An  iron  disk  weighing  100  g.  is  suita- 
ble.    It  should  have  one  face  covered  with  paper  to  avoid  its  cling- 
ing to  the  magnet  poles  when  the  circuit  is  open.) 

Procedure  : 

(a)  The  battery  is  connected  in  circuit  with  the  key  and  electro- 
magnet.    The  key  is  closed,  and  the  iron  weight  is  carefully  adjusted 
upon  the  poles  of  the  magnet. 

(b)  The  magnet,  with  the  weight  still  clinging  to  it,  is  hoisted  by 
means  of  the  cord  to  a  position  just  below  the  bracket,  such  that  the 
weight  will  be  490  cm.  above  the  floor,  or,  better,  above  a  block  or 
pad   placed  vertically  below  the  bracket.     The   magnet  must  be  so 
attached  to  the  cord  as  to  swing  freely,  as  shown  in  the  figure,  with 
the  weight  lowermost. 

(c)  The  metronome  is  started,  and  the  observer,  with  his  finger 
upon  the  key,  opens  the  circuit  promptly  at  a  stroke  of  the  former. 
Note  how  accurately  the  blow  of  the  falling  disk  corresponds  with  the  next 
stroke  of  the  metronome. 

The  observation  is  of  the  simplest  character,  but  it  affords  evidence 
of  the  most  direct  nature  concerning  the  distance  through  which  a 
body  falling  freely  passes  in  one  second. 


GRAVITATION  31 


CHAPTER  IV 
GRAVITATION  IN   COMBINATION  WITH  OTHER  FORCES 

29.  Projectiles,  —  A  projectile  is  a  body  which  has  been 
given  an  initial  velocity  by  being  thrown  from  a  gun  or 
bow,  or  from  the  hand,  or  in  any  other  manner.     It  fol- 
lows a  path  which  depends  upon  the  size  and  direction  of 
this  initial  velocity,  and  upon  the  action  of  gravitation, 
and   of  such   other  forces   as   may  be   brought   to   bear 
upon  it. 

Since,  as  we  have  seen  (Art.  26),  gravitation  acts  in 
precisely  the  same  way  upon  bodies,  whether  they  be 
at  rest  or  in  motion,  we  may  apply  to  projectiles  the  laws 
of  bodies  falling  freely  from  a  state  of  rest. 

30.  EXAMPLE  1.    (Initial  velocity  horizontal.')  —  Given  a 
body,  P,  with  an  initial  velocity,  Vh  (Fig.  22).     The  earth 
acts  upon  it  with  a  vertical  force,  v 

the  acceleration  due  to  which  is    ' 
represented  by  g.      To  find  the 
position  of  the  body  at  the  end 
of  1,  2,  3,  4,  etc.,  seconds. 

Were  P  at  rest,  it  would  fall  in  1,  2,  3,  4,  etc.,  seconds 
to  positions  y^  yv  yy  y±,  etc.,  vertically  below  p  (Fig.  23). 
Freed  from  the  action  of  the  earth,  however,  P,  on  account 
of  its  initial  velocity,  would  move  to  x1  in  1  sec.,  x2  in  2 
sec.,  x3  in  3  sec.,  etc.  Its  positions  under  the  combined 
actions  of  its  own  velocity  and  of  gravitation  will  be 
respectively  pv  p^  p%,  p#  etc. 


32 


THE   OUTLINES   OF  PHYSICS 


The  curve  drawn  through  these  points  is  the  path  of  the 
projectile  P.  It  is  a  parabola,  as  is  indeed  the  path  of 
any  projectile  subjected  to  a  constant  force. 


1/2 


FIG.  23. 

31.  EXAMPLE  2.  (Initial  velocity  oblique.}  —  The  same 
construction  is  used  as  in  Example  1,  save  that  the  line 
pv^  along  which  the  component  of  motion  due  to  initial 
velocity  is  laid  off,  is  oblique  and  has  the  same  direction 
as  the  latter.  (See  Fig.  24.)  The  trace  or  path  is  para- 
bolic. 

As  before,  yv  y^  y%,  y±  are  the  successive  positions 
which  would  be  reached  in  1,  2,  3,  and  4  seconds,  un- 


GRAVITATION 


33 


der  gravitation  alone.  The  positions  vv  vv  vy 
spond  to  xv  Xy  xy,  x±  of  Example  1.  They  are  the  posi- 
tions which  would  be  reached  were  no  forces  to  modify 
the  motion  of  p.  The  po- 
sitions actually  reached  are 

Pv  Pv  Pv  Pv 


32.  EXAMPLE  3.  (Initial 
velocity  vertical.)  —  There 
are  two  cases ;  of  upward 
and  of  downward  initial 
velocity,  respectively,  but 
both  are  solved  by  the  sim- 
ple numerical  process  of 
computing  the  position 
which  would  have  been 
occupied  had  gravitation 
not  acted,  and  the  position 
in  case  the  initial  velocity 
had  been  zero. 

These  are  subtracted 
when  the  initial  velocity 
is  upwards,  and  added 
when  it  is  downwards. 

Given  an  upward  initial 
velocity  of  1000  cm.  per 
second:  to  find  the  posi- 
tion of  the  projectile  after 
3  seconds  (#=980). 

Without  gravitation  its 
position  would  be  3000  cm. 
above  the  starting  point. 

Gravitation,  but  for  the 


FIG.  24. 


34  THE  OUTLINES   OF  PHYSICS 

initial  velocity,  would  carry  it  downwards  over  a  path  s, 
such  that 

*  =    ? 


P3,  the  new  position,  is  4410  —  3000  =  1410  cm.  below 
the  starting  point. 

Had  the  initial  velocity  been  1000  cm.  downward  the 
new  position  would  have  been  found  at  4410  -f-  3000  = 
7410  cm.  below  the  starting  point. 

33.  The  Ballistic  Curve.  —  Thus  far  we  have  considered 
projectiles   moving   under   a   single    constant   force.      In 
reality,  however,  projectiles  are  subjected  to  other  forces, 
such  as  the  ordinary  resistance  of  the  atmosphere  and  the 
force  of  the  wind.     These  modify  the  path  of  the  projec- 
tile and  cause  it  to  deviate  from  the  parabolic  form.     In 
the   case  of   projectiles  of   high  speed  this  divergence  is 
considerable,   and   it   has   to   be   taken  accurate   account 
of  in  the  science  of  gunnery.     Along  parabolic  paths,  for 
example,  in  order  to  carry  a  shot  to  the  greatest  distance, 
the  elevation  of  the  gun  must  be  45°  above  the  horizon  ; 
whereas  experiments  with  various  weapons  give  for  the 
maximum  range  very  different  angles,  sometimes  as  low 
as  30°. 

That  for  projectiles  of  low  speed  the  ballistic  curve  is 
very  nearly  parabolic,  the  following  experiment  will  serve 
to  show  : 

34.  EXPERIMENT  4.  —  Plotting  the  Ballistic  Curve  of  a  Water  Jet 
and  Comparison  of  the  Same  with  the  Parabola. 

Apparatus  : 

(1)  A  blackboard. 

(2)  A  long  rubber  tube  of  0-5  cm.  to  I'O  cm.  bore  leading  from  an 


GRAVITATION  35 

elevated  tank  to  the  neighborhood  of  the  board.  It  is  provided  with 
a  nozzle  consisting  of  a  glass  tube  drawn  out  at  one  end  until  the  bore 
is  reduced  to  about  0*2  cm.  It  is  also  provided  with  a  pinchcock  to 
stop  the  flow. 

(3)  A  wooden  scale  divided  to  centimeters. 

Procedure : 

(a)  Adjust  the  pressure  so  that  the  jet,  when  the  nozzle  is  held 
horizontally  near  the  top  of  the  blackboard,  will  have  a  velocity 
sufficient  to  carry  it  a  meter  or  more  before  it  reaches  the  level  of 
the  base  of  the  blackboard. 

o 


FIG.  25. 

(b)  Hold  the  nozzle  in  the  position  indicated  above,  the  plane  of 
the  jet  parallel  to  the  blackboard.      Then  give  the  nozzle  a  single 
slight  inward  motion  with  the  hand  so  as  to  wet  the  board.     With 
a  little  practice  it  will  be  found  possible  to  obtain  a  fairly  good  trace 
of  the  jet  upon  the  board,  which  can  then  be  perpetuated  by  outlin- 
ing it  with  the  chalk.     The  position  of  the  nozzle  should  also  be 
indicated. 

(c)  After  the  board  has  become  dry,  draw  from  the  point  where 
the  jet  may  be  considered  to  have  its  origin  (point  corresponding  to 
the  tip  of  the  nozzle)  a  vertical  line  oy   and   a   horizontal  line  ox. 
Extend  the  former  to  a  point  near  the  bottom  of  the  board  and  divide 
it  into  16  equal  parts.     From  divisions  1,  4,  9,  and  16,  draw  horizontal 


36  THE  OUTLINES  OF  PHYSICS 

lines  to  intersect  the  trace  of  the  jet.  From  the  intersections  draw 
vertical  lines  to  cut  the  horizontal  line  ox. 

Were  the  curve  a  parabola,  these  intersections  of  the  verticals  with 
ox  would  be  equidistant,  as  in  Fig.  23,  with  which  the  diagram  just 
obtained  should  be  compared.  Note  the  amount  and  character  of  the 
discrepancy.  For  such  small  velocities  the  deviation  from  the  para- 
bolic form  should  be  insignificant. 

Figure  25  shows  the  trace  of  a  water  jet  obtained,  not  by  the 
method  described  above,  but  by  photographing  the  jet  itself  against 
a  black  background.  The  points  of  the  corresponding  p'arabola  have 
been  drawn  in.  It  will  be  seen  that  they  lie  very  close  indeed  to  the 
path  of  the  jet. 


THE  SIMPLE  PENDULUM 


37 


CHAPTER   V 

THE   SIMPLE   PENDULUM 

35.  The  Pendulum.  —  Given  a  body  B  (Fig.  26),  rigidly 
attached  to  a  point  0  about  which  it  is  free  to  revolve. 
Such  a  body,  when  acted  upon  by  a  constant  force  as  </, 
tends  to  come  to  rest  in  a  position  such 
that  g  is  parallel  to  the  line  OB.  This 
position,  which  is  represented  by  the 
dotted  lines  in  the  figure,  is  called  the 
position  of  stable  equilibrium.  When 
removed  from  this  position  and  then 
released,  the  body  goes  through  a 
series  of  oscillatory  motions,  the  laws 
of  which  are  to  be  experimentally  de- 
termined. Such  a  body  is  called  a 
pendulum.  The  simplest  case  is  that 
of  a  single  material  point  attached  to 
the  center  of  oscillation  0,  by  means  of 
a  rigid  thread  without  mass.  Such  a 
pendulum  is  called  the  mathematical 
pendulum  (sometimes  called  the  sim- 
ple pendulum).  Pendulums  which  do 
not  fulfill  the  above  condition  are  termed  physical  pendu- 
lums. The  term  simple  pendulum  will  be  used  in  this 
book,  however,  to  designate  any  pendulum  in  which  the 
mass  is  chiefly  concentrated  in  a  compact  ball  or  bob,  sus- 
pended by  a  wire  or  rod. 


FIG.  26. 


38  THE  OUTLINES   OF  PHYSICS 

36.  Definition  of  Terms  referring  to  the  Pendulum. 

Center  of  suspension.  —  The  point  around  which  a  simple 
pendulum  oscillates.  In  the  case  of  a  physical  pendulum, 
with  freedom  of  motion  in  a  single  plane,  there  is  a  line 
or  axis  around  which  it  swings.  This  is  the  axis  of 
suspension. 

Center  of  oscillation.  —  A  point  at  which  all  the  material 
of  a  physical  pendulum  may  be  considered  as  concentrated 
without  affecting  its  rate. 

Length.  —  The  distance  from  center  of  suspension  to 
center  of  oscillation. 

Period.  —  The  time  in  seconds  between  successive  pas- 
sages of  the  pendulum  through  its  position  of  equilibrium. 
This  is  the  period  of  a  single  oscillation. 

Double  period. — The  time  in  seconds  which  elapses 
from  the  instant  when  a  pendulum  is  at  its  turning  point, 
on  either  side  of  its  position  of  equilibrium,  until  it 
reaches  the  turning  point  upon  the  same  side  again. 

Hate.  —  The  number  of  single  oscillations  performed  by 
a  pendulum  in  one  second. 

Amplitude.  —  The  path  traversed  by  the  pendulum  in 
its  motion.  (Amplitude  is  measured  in  seconds,  minutes, 
or  degrees  of  arc.) 

37.  EXPERIMENT  5.  —  Law  of  the  Simple  Pendulum. 

Apparatus : 

(1)  Two  small  leaden  balls,  also  one  of  iron  or  brass,  and  one  of 
wood.     These  are  preferably  all  of  a  size  and  about  4  cm.  in  diameter. 
If  they  are  bored  through  diametrically,  with  a  hole  large  enough  to 
admit   a  thread  or  small   cord,  it  adds   to   the   convenience  of  the 
operations. 

(2)  Several  meters  of  strong  thread  or  twine  (the  braided  linen  or 
silk  cords,  manufactured  for  fishing  lines,  are  much  the  best). 

(3)  A  stand  consisting  of  a  substantial  base,  an  upright,  and  a 


THE  SIMPLE  PENDULUM 


39 


horizontal  arm.     The  arm  should  be  40  cm.  or  more  in  length  and 
must  be  situated  at  least  110  cm.  above  the  base.     It  should  contain 


0  0 


FIG.  27. 

four  vertical  holes,  running  quite  through,  and  distant  about  10  cm. 
from  one  another  and  from  the  upright.  The  diameter  of  these  holes 
should  be  about  0-1  cm.  The  horizontal  arm  should  be  fastened  to  the 
upright  by  mortising,  in  such  a  manner  that 

one  half  of  its  thickness  projects  beyond  the     ffjD — — 1 

edge  of  the  latter  as  in  Fig.  28.     The  holes 

through  the  arm  will  then  be  in  the  same 

vertical  plane  with  the  edge  of  the  upright,  an  arrangement  which 

greatly  facilitates  the  measurements. 

(4)  A  clock,  the  pendulum  of  which  beats  seconds,  or  a  metronome. 

(5)  A  meter  scale. 


FIG.  28. 


40 


THE  OUTLINES   OF  PHYSICS 


Procedure : 

(a)  By  means  of  small  wooden  plugs,  fasten  about  110  cm.  of 
twine  to  each  of  the  balls,  passing  the  free  ends  up  through  the  holes 
in  the  arm  and  securing  them  there  by  means  of  similar  plugs. 
These  last  should  be  inserted  from  below.  They  should  fit  in  such  a 
way  as  to  check  the  motion  of  the  cord  at  the  base  of  the  opening, 
and  yet  permit  it  to  be  drawn  through  from  above  or  below.  After 
adjustment  for  length  has  been  made,  the  cord  may  be  further 
secured  by  means  of  a  short  peg  inserted  at  the  top  of  each  hole. 

Attach  the  wooden  ball  nearest  the  upright,  then  the  iron  or  brass 
balls,  then,  outermost,  the  two  leaden  balls. 

(ft)  Adjust  the  lengths  of  the 
suspension  cords  until  the  pendu- 
lums all  swing  in  as  nearly  as  pos- 
sible the  same  time.  Note  that  the 
lengths  are  then  all  the  same.  Note, 
further,  that  the  wooden  ball  comes 
to  rest  much  sooner  than  do  the 
metal  balls,  and  that  the  leaden  balls, 

r\^~~ ' —  I-  -i    w^h  their  greater  density,  have  the 

I       I        I        I        I       ^~|_        greatest  persistence  of  motion. 

E— '  (c)  Shorten  the  suspension  of  one 

/  of  the  leaden  balls  until  it  swings 

'  twice  as  rapidly  as  does  the  other. 

FIG.  29.  0, 

Show    by    measurement    that    the 

lengths  of  the  two  pendulums  are  as  1  :  4.  (In  making  the  measure- 
ment of  lengths,  measure  from  a  line  tangent  to  the  ball  above  [see 
Fig.  29]  to  the  top  of  the  suspension  cord.  Then  add  the  radius  of 
the  ball.)1 

1  The  true  length  of  the  pendulum  is  not  the  distance  from  the  center 
of  suspension  to  the  middle  of  the  ball,  but  that  distance  is  sufficiently 
exact  for  the  purposes  of  the  present  determination.  The  length  I  is 


where  X  is  the  distance  from  the  center  of  suspension  to  the  top  of  the 

ball,  and  r  is  the  radius  of  the  ball.     For  a  pendulum  100  cm.  long,  with 

2  r2 
a  ball  2  cm.  radius,  -*  —  is  0-016  cm.,  and  for  a  pendulum  25  cm.  long, 

with  the  same  ball,  it  is  -064. 


THE  SIMPLE  PENDULUM  41 

(d)  From  this  relation  of  times  to  lengths  determined  in  (c),  viz. 
1,:12::  1:4, 
*,:<,::  1:2, 

it  is  reasonable  to  assume  as  the  law  of  lengths,  that  the  square  of  the 
time  of  vibration  of  a  pendulum  is  proportional  to  its  length.  Verify 
this  assumption  by  making  the  length  of  the  shorter  pendulum  |  of 
that  of  the  longer  one,  in  which  case  the  times  will  be  found  to  have 
the  ratio  2  :  3. 

38.  The  Law  of  Equal  Times. — Thus  far  we  have  assumed 
that  the  arc  of  vibration  of  a  pendulum  is  without  influ- 
ence upon  its  rate.     This  assumption  can  be  shown  to  be 
true  with  an  exactitude  sufficient  for  the  purposes  of  these 
experiments.     The  law  of  equal  times,  or,  as  it  is  called, 
the  law  of  isochronism,  is  in  fact  only  an  approximation ; 
vibrations  of  large  amplitude  requiring  a  slightly  longer 
time  than  those  of  small  amplitude.     The  differences  are 
such  as  require  refined  methods  for  their  detection.     For 
example,  a  vibration  of  infinitesimal  amplitude,  requiring 
1  second,  will  have  a  period  of  1-008  (nearly)  when  the 
amplitude  is  increased  to  20°. 

The  approximate  accuracy  of  the  law  of  equal  times 
may  be  verified  as  follows : 

39.  EXPERIMENT  6.  —  Isochronism  of  the  Pendulum. 

Apparatus : 

(1)  The  pendulum  stand  described  in  Experiment  5,  and  the  long 
pendulum  with  a  leaden  bob. 

(2)  The  metronome.1 
Procedure  : 

(a)  The  observer,  who  is  seated  opposite  the  pendulum,  with  the 
plane  of  vibration  at  right  angles  with  his  line  of  sight,  directs  his 
vision  to  a  vertical  mark  previously  made  upon  the  upright  of  the 
pendulum  stand.  Past  this  swings  the  pendulum,  which  has  been 
adjusted  to  a  period  which  is  very  nearly  an  exact  second. 

1  A  loud-ticking  clock  which  beats  seconds  will  do  as  well. 


42  THE  OUTLINES  OF  PHYSICS 

(6)  He  watches  until  the  pendulum  passes  the  mark,  at  the  beat  of 
the  metronome,  and  then  begins  to  count  seconds,  continuing  to 
count  until  the  pendulum  is  on  the  mark  again  at  the  sound  of  that 
instrument.  The  time  which  has  elapsed  between  these  coincidences 
is  that  required  by  the  pendulum  to  gain  one  beat  over  the  metro- 
nome, or  vice  versa.  It  is  only  necessary  to  note  further  whether  the 
pendulum  gains  or  loses  with  reference  to  the  metronome,  in  order  to 
compute  the  relative  period  of  the  former. 

Example:  Suppose  the  pendulum  to  be  losing,  and  that  the  ob- 
served interval  between  coincidences  is  59  seconds.  It  makes  58 
beats  in  59  seconds  (since  it  has  made  one  less  than  the  metronome), 
and  its  period  is  f  f  seconds  =  1*0173  seconds  nearly. 

(c)  This  observation  of  coincidences  is  to  be  repeated  several 
times  with  amplitudes  of  about  20°,  5°,  and  less  than  1°  respectively. 

40.  The  Method  of  Coincidences.  —  The  method  described 
above  is  much  more  accurate  than  the  laborious  method  of 
counting  the  total  number  of  vibrations  in  a  given  interval 
of  time ;    and  the  likelihood  of   mistaking  the  count  is 
much  less  than  where  a  large  number  of  vibrations  has  to 
be  observed.     It  is  known  as  the  method  of  coincidences. 

41.  EXPERIMENT  7. — Relation  of  the  Rate  of  a  Peclulum  to  the 
Force  under  the  Action  of  which  it  swings. 

[For  the  purpose  of  this  determination  we  use  the  same  expedient 
as  in  a  previous  case  (experiment  of  the  inclined  plane  [Art.  25]); 
that  of  resolving  gravitation  into  two  forces,  only  one  of  which  acts  to 
produce  motion.] 

Apparatus  : 

(1)  The  pendulum  stand  described  in  Experiment  5. 

(2)  A  protractor  or  other  device  for  the  rough  measurement  of 
angles. 

(3)  A  watch  or  other  timepiece  with  a  second  hand. 

(4)  A  pendulum  of  the  form  shown  in  Fig.  30.     It  consists  of  a 
piece  of  stiff  wire  a,  b,  c,  d,  bent  as  shown  in  the  figure.     The  ends 
a,  d  are  soldered  together  and  pass  through  the  hole  in  one  of  the 
metal  balls  described  in  Experiment  5.      The  ball  is  fastened  by 


THE  SIMPLE  PENDULUM 


43 


means  of  plugs.  At  b,  c,  is  fastened,  either  by  soldering  or  by  lashing 
firmly  with  thread,  a  piece  of  steel  wire  (part  of  a  knitting  needle, 
ground  to  points  at  the  ends)  which  serves  as  an  axis  of  suspension. 

The  pendulum  is  mounted  in  a 
joiner's  clamp,  as  shown  in  Fig.  31 ; 
small,  smooth,  conical  holes  being 
made  in  the  end  of  the  wooden 
screw,  and  in  a  corresponding  posi- 


FIG.  30. 


FIG.  31. 


tion  in  the  inner  face  of  the  jaw  of  the  clamp  (viz.  in  the  line  of  the 
axis  of  the  screw  continued).  The  axis  of  suspension  of  the  pendu- 
lum should  bear  only  at  the  points  and  not  on  the  periphery  of  the 
wire. 

Procedure : 

(a)  Mount  the  pendulum  vertically,  clamping  it  to  the  pendulum 
stand,  as  shown  in  Fig.  31.  Determine  to  the  nearest  second  the  time 
required  for  one  hundred  oscillations.  Repeat  the  observation  at  least 
five  times  and  average  the  results. 

(6)  Mount  the  pendulum  at  45°,  as  shown  in  Fig.  32,  and  thus 
resolve  g  into  two  equal  components,  a  and  6,  only  one  of  which,  the 
component  a,  tends  to  produce  oscillation. 

The  component  a  is  to  g  as  7  : 10,  nearly  (more  accurately  7-07  to 
10).  It  is  the  object  of  the  observation  to  verify  the  fact  that  the 


44 


THE   OUTLINES   OF  PHYSICS 


square  of  the  rate  of  the  pendulum  in  this  new  position  bears  the 
above  ratio  to  the  square  of  its  rate  when  mounted  vertically. 
The  relation  between  force  and  period  is  as  follows : 

—  :  —  : :  a  :  a. 

f  2     /  2        y 

ig     ia 

in  which  the  period  under  action  of  the  force  corresponding  to  g  is 
designated  by  tg,  and  the  period1  under  the  action  of  a,  by  ta.  The 
law  may  be  stated  thus : 

The  square  of  the  rate  of  a  pendulum  is  proportional  to  the  force  to 
which  its  oscillations  are  due. 

(c)  Verify  the  law  for  an  angle  of  60°  (at  this  inclination  a  =  $g) . 


FIG.  32. 

1  The  general  relation  of  g  to  a  is  expressed  in  the  formula 

a  =  gcosa, 

where  a  is  the  angle  which  the  line  joining  centers  of  suspension  and  of 
oscillation  makes  with  the  vertical  line  through  the  former. 


THE  SIMPLE  PENDULUM  45 

42.    Summary  of  the  Results  of  Experiments  5,  6,  and  7. 

(1)  The  period  of  oscillation  of  a  simple  pendulum  is 
independent  of  the  material  of  which  the  bob  is  made,  and 
also  of  the  mass  of  the  bbbv 

(2)  The  square  of  the  period  of  oscillation  is  propor- 
tional to  the  length  of  the  pendulum. 

(3)  The  period  is   approximately  independent  of   the 
amplitude  of  oscillation. 

(4)  The  square  of  the  period  of  oscillation  is  inversely 
proportional  to  the  force  to  which  the  oscillations  are  due. 

These  results  may  be  gathered  into  a  formula  which 
states  what  is  generally  called  the  law  of  the  simple 
pendulum,  viz. : 

t  =  7T  >/-. 

^g 

In  this  expression  t  is  the  period  in  seconds ;  I  is  the 
length  in  centimeters ;  g  is  the  acceleration  due  to  the  force 
of  gravitation  (or  of  whatever  "force  produces  the  oscilla- 
tions), also  measured  in  centimeters ;  TT  is  the  ratio  of  the 
circumference  of  a  circle  to  its  diameter,  viz.  3-14159  -f. 
This  formula  applies  to  any  pendulum  whether  simple  or 
not,  provided  I  is  always  taken  to  be  the  distance  between 
the  centers  of  suspension  and  oscillation. 

By  means  of  it  we  can  compute  : 

(1)  The  length  of  a  pendulum  which  will  beat  seconds, 
In  any  locality  where  g  is  known. 

(2)  The  rate  of   any  pendulum,  of   whatever  length, 
where  g  is  known. 

(3)  The  value  of  g,  in  any  locality  where  it  is  unknown, 
from  the   period  of  vibration  of  a  pendulum  of  known 
length. 

This  last  is  an  operation  of  the  greatest  importance  in 
physics,  since  it  is  by  means  of  it  that  our  knowledge  of 


46 


THE  OUTLINES   OF  PHYSICS 


variations  in  the  force  of  gravitation  in  different  parts  of 
the  world  has  been  gained. 

43.    EXPERIMENT  8.  —  Testing  a  Metronome  by  Comparison  with 
a  Seconds  Pendulum. 

Apparatus  : 

(1)  The  pendulum  stand  already  described,  and  the  pendulum  with 
a  leaden  ball. 

(2)  A  meter  scale. 

(3)  A  metronome. 

Procedure  : 

(a)  Measure  the  diameter  of  the  ball. 

(b)  Suspend  the  ball  by  a  string  or  wire,  making  the  length  of 

the  string,  plus  half  the  diameter  of  the  ball,  equal  to 
99-3  cm.  (The  pendulum  thus  constructed  will  have 
a  period  of  almost  precisely  one  second.) 

(c)  Mount  just  behind  the  suspension  wire  of  the 
pendulum  a  card  with  a  heavy   vertical   black   line 
marked  upon  it. 

(d)  Sit  directly  in  front  of  the  pendulum,  the  eye 
nearly  on  a  level  with  the  card,  and  the  head  in  such 
a  position  that  the  suspension  wire,  when  at  rest,  will 
coincide  with  the  vertical  line.     Pull  the  ball  to  one 
side,  about  two  or  three  degrees  (i.e.  about  5  cm.), 
parallel  to  the  card,  and  release  it.      Listen  to  the 
metronome,  previously  set  at  60  beats  a  minute,  and 
at  the  same  time  watch  the  suspension  wire.     Note 
the  successive  positions  which  it  occupies  at  each  beat 
of  the  metronome,  and  thus  determine  whether  the 
metronome  is  gaining  or  losing  with  reference  to  the 
pendulum.     If  the  metronome   is  gaining,  the  posi- 
tion of  the   suspension  wire  at  successive  beats  will 
be  displaced  in  a  direction  opposite  to  the  movement 
of  the  pendulum,  as  indicated  in  Fig.  33.      If  the 

FlG  33  metronome  is  losing^  the  reverse  will  be  true. 

(e}  Having  determined  whether  the  metronome  is 
gaining  or  losing,  watch  the  position  of  the  suspension  wire  again, 
and  when  the  wire  is  coincident  with  the  mark  behind  the  pendulum, 


d 


THE  SIMPLE  PENDULUM  47 

at  the  tap  of  the  metronome  begin  to  count  the  beats  of  the  latter. 
Continue  to  count  until  the  wire  coincides  with  the  mark  again, 
and  then  record  the  number  of  beats  which  have  intervened. 

Compute  from  this  interval  the  relative  rates  of  the  pendulum 
and  the  metronome.  If,  for  example,  the  metronome  is  gaining, 
and  it  makes  65  beats  from  coincidence  to  coincidence,  then  its 
rate  is  f  £  beats  per  second,  or  its  period  (single)  is  ff  seconds  = 
0-984+  seconds.  This  is  obvious  since  the  interval  between  coinci- 
dences is  that  required  by  the  metronome  to  gain  one  beat. 

If  the  metronome  is  losing,  on  the  other  hand,  and  the  interval 
between  coincidences  is  65,  its  rate  must  be  ff  beats  per  second,  and 
its  period  ff  seconds  =  1-016+  seconds. 

(/)  If  a  clock  with  a  pendulum  which  beats  seconds  is  available, 
find  the  rate  of  the  metronome,  as  compared  with  the  clock,  by  the 
method  of  coincidences.  This  part  of  the  experiment  is  not  a  mere 
repetition  of  what  has  gone  before,  since  it  is  to  be  performed  entirely 
by  the  ear.  The  process  consists  in  listening  simultaneously  to  the 
ticking  of  the  clock  and  the  metronome  until  they  beat  in  unison, 
and  then  in  counting  the  beats  of  the  latter  until  unison  is  reached 
again. 

Students  who  have  the  time  arid  patience  to  cope  with  somewhat 
greater  difficulties  than  are  demanded  by  this  determination,  may  try 
the  following  very  interesting  and  instructive  experiment : 

44.    EXPERIMENT  9.  —  Approximate  Length  of  a  Pendulum  which 
beats  Seconds. 
Apparatus : 

(1)  A  pendulum  with  leaden  ball.     (Experiment  5.) 

(2)  A  meter  scale. 

(3)  A  metronome.     (Experiment  5  [e].) 

To  obtain  the  best  results  in  this  determination,  a  fine  wire  of 
iron  or  brass  should  be  used  instead  of  the  suspension  cord.  This, 
at  the  upper  end,  should  be  held  within  the  jaws  of  a  hand  vise, 
which,  in  turn,  is  clamped  to  the  horizontal  arm  of  the  pendulum 
stand.  Thus  a  much  more  definite  point  from  which  to  measure 
lengths  is  obtained. 

Procedure : 

(a)  Measure  the  diameter  of  the  ball. 

(6)  Adjust  the  pendulum  to  a  length  of   about  105  cm.     Deter- 


48 


THE   OUTLINES   OF  PHYSICS 


mine  its  rate  by  the  method  of  coincidences.  Measure  the  length  to 
the  upper  periphery  of  the  ball. 

(c)  Repeat  the  above  observations  of  rate  and  length  with  the 
pendulum  set  approximately  at  103  cm.,  101  cm.,  99  cm.,  and  97  cm.,  etc. 

(cT)  Tabulate  the  results  as  shown  below. 


TABLE  :   LENGTH  OP  A  SECONDS  PENDULUM. 


Obs. 

Time  in  beats 
of  the  metro- 
nome from 
coincidence  to 
coincidence. 

Eate. 

Period  from 
each  set. 

Lengths 
(observed). 

Lengths  1 
(corrected). 

a 

22 

fl 

if  =  1-045 

103-4  cm. 

105-8  cm. 

b 

33 

if 

fl  =  1-0312 

101-7    " 

104-1    " 

c 

53 

e 

|f  =  1-0192 

99-5    " 

101-9    " 

d 

400 

m 

f$£  =  0-9076 

95-0    " 

97-4    " 

e 

91 

f! 

|-i  =  0-989 

93-4    » 

95-8    " 

(e)  To  determine  from  these  measurements  the  length  of  a  pendu- 
lum, the  period  of  vibration  of  which  would  be  the  same  as  that  of 
the  metronome,  take  a  piece  of  cross-section  paper  and  mark  along 
the  base  (as  abscissas)  times  in  seconds,  and  along  the  vertical  edges 
(as  ordinates)  lengths  as  shown  in  Fig.  34.  (See  Appendix  II.) 

Find  the  points  on  this  sheet  corresponding  to  corrected  lengths 
and  rates,  for  sets  a,  b,  c,  d,  e,  etc.,  respectively. 

These  will  lie  approximately  in  an  oblique  line  (strictly  speaking 
along  a  curve ;  the  curvature  of  which  is  so  slight,  within  the  limits 
of  this  experiment,  as  to  be  scarcely  perceptible).  Wide  divergence 
of  one  of  the  values  from  the  line  joining  the  others  indicates  a  blun- 
der. If  the  values  do  not  lie  so  that  a  nearly  straight  line  can  be 
drawn  through  them,  the  experiment  has  been  poorly  performed. 

A  certain  amount  of  divergence  is  to  be  expected  among  experi- 
mental results,  however  painstaking  the  observer  may  be.  Thus  it 
will  be  seen  in  Fig.  34  that  the  points  a,  6,  c,  d,  and  e  do  not  lie  upon 

1  These  lengths  are  obtained  by  adding  to  the  observed  length  the 
radius  of  the  ball,  which,  in  the  case  to  which  these  data  refer,  was 
2-4  cm. 


THE  SIMPLE  PENDULUM 


49 


a  common  line.     They  do,  however,  lie  near  a  line  mn,  drawn  in  such 
a  way  as  to  equalize  the  divergence  as  far  as  possible. 


/?i 

/ 

a 

/ 

104  c 

n. 

b/ 

/ 

C 

/ 

/ 

100  c 

u. 

/ 

co 

I 
h- 

B 

XP 

| 

V 

y 

96  cr 

a. 

/ 

' 

Q 

r 

| 

92  ci 

a. 

A 

TIIV 

ES 

8s.                               1.00s.                               1.02s.                              1.04s. 
FIG.  34. 

Draw  such  a  line  through  the  group  of  observation  points,  after 
the  latter  have  been  marked  upon  the  paper.  Note  the  reading  of 
the  intersection  of  this  line  with  the  ordinate  corresponding  to  1  second. 


50  THE  OUTLINES   OF  PHYSICS 

This  reading  is  the  length  of  the  pendulum  beating  in  unison  with 
the  metronome,  as  determined  by  this  experiment. 

Systematic  Errors.  —  The  divergence  of  the  observation "  points  a,  b, 
c,  d,  etc.,  from  line  mn  is  called  in  each  case  the  error  of  observation  or 
the  accidental  error.  There  may  be  sources  of  error,  however,  which 
would  cause  the  entire  group  to  have  too  large  or  too  small  values. 
Such  errors  are  called  systematic  errors.  In  this  experiment,  for  ex- 
ample, the  metronome  might  be  running  very  fast  or  very  slow,  so 
that  it  did  not  beat  exact  seconds ;  or  the  scale  might  not  be  a  true 
meter,  or  the  observer  might  measure  from  the  wrong  level  at  the  top 
of  the  pendulum.  Or  he  might  use  a  wrong  value  for  the  radius  of 
the  ball  in  correcting  the  lengths.  All  of  the  above  would  affect  the 
entire  series  of  observations.  In  the  present  case  we  can  detect  the 
size  and  direction  of  the  first  of  these  systematic  errors,  that  due  to 
the  rate  of  the  metronome,  by  computing  the  length  of  a  pendulum 
which  would  beat  seconds,  and  representing  the  result  graphically 
upon  the  same  sheet  with  the  experimental  curve.  For  this  purpose 
we  use  the  formula 

t  = 
which  solved  for  I  gives  us 


A  value  of  g  nearly  enough  correct,  in  most  localities,  for  the  pur- 
pose of  this  computation  is  g  =  980-5  cm.,  which  is  the  acceleration 
due  to  gravitation  in  latitude  45°  at  the  level  of  the  sea. 

This  gives  for  /,  since  t2  —  1,  and  7r2  =  9-870, 


Represent  this  result  upon  the  cross-section  paper  by  means  of  a 
vertical  line  AB,  extending  from  the  point  (A)  upon  the  base  line 
which  corresponds  to  1  second,  to  (B)  at  the  height  corresponding  to 
99-34  cm. 

Draw  the  horizontal  line  Bp.  This,  expressed  in  seconds,  will  give 
the  error  of  the  metronome.  For  example,  in  the  case  given  for 
illustration  in  Fig.  34.  One  true  second  =  1-007  seconds  by  the  metro- 

nome, whence  we  conclude  that  the  period  of  the  latter  is  -  = 

1*007 
0-9993. 


THE  PHYSICAL  PENDULUM  51 


CHAPTER  VI 

THE  PHYSICAL  PENDULUM 

45.   EXPERIMENT  10.  —  To  find  by  Experiment  the  Center  of  Oscil- 
lation. 

Apparatus : 

(1)  The  pendulum  stand  and  one  of  the  pendulums  with  leaden 
ball  described  in  Experiment  5. 

(2)  A  physical  pendulum  consisting  of  a  straight  cylindrical  rod 
or  bar,  preferably  of  iron  or  brass,  about  one  meter  long.     It  should  be 
of  the  same  material  throughout.     The  axis  of  suspension  of  this 
pendulum  consists  of  a  piece  of  steel  wire,  pointed,  as  described  in 
Experiment  7.     It  should  be  soldered  to  one  end  of  the  cylinder, 
especial  pains  being  taken  that  the  axis  of  suspension  passes 
through  the  axis  of  the  cylinder  and  is  perpendicular  to  the     -y-|— 
same  (Fig.  35). 

The  cylindrical  pendulum  may  be  suspended  from  a 
joiner's  clamp,  prepared  as  in  Experiment  7. 

Procedure: 

(a)  Hang  the  simple  pendulum  and  the  physical  pendu- 
lum side  by  side  (Fig.  36),  and  adjust  the  length  of  the 
former  until  the  two  swing  as  nearly  as  possible  in  the  same 
time. 

(&)  Measure  the  length  of  the  simple  pendulum  as  pre- 
scribed in  Experiment  5,  and  make  the  correction  for  the 
true  value  of  I.  That  length,  measured  from  the  axis  of 
suspension  of  the  physical  pendulum  along  the  axis  of  the 
cylinder,  determines  the  position  of  its  center  of  oscillation. 

Measure  the  length  of  the  cylinder  and  state  the  distance  FIG.  35. 
(/)  of  the  center  of  oscillation  from  the  axis  of  support  in 
terms  of  the  total  length,  L. 

Compare  your  result  with  the  position  which  would  be  given  by 


52 


THE   OUTLINES   OF  PHYSICS 


computation   under  the   assumption    that   the   cylinder  is  homoge- 
neous.1 

The  above  experimental  method  is  applicable  to  any  physical  pen- 
dulum, whatever  its  form.  The  cylindrical  bar  is  selected  because 
the  result  can  be  checked  by  computation. 


FIG.  36. 

1  The  distance  between  axis  of  suspension  and  center  of  oscillation  of 
a  thin  bar  swinging  from  one  end  is 

l  =  |Z. 

The  formula  is  I  =  _,  where  K  is  the  moment  of  inertia  of  the  bar, 

mx 
m  is  its  mass,  and  x  is  the  distance  of  the  center  of  mass  from  the  axis  of 

suspension.     K,  however,  is  m-,  and  x  is  \  L.     (See  Nichols  and  Franklin, 

3 
Elements  of  Physics,  Vol.  I,  pp.  66  and  75.) 


THE  PHYSICAL  PENDULUM 


53 


46.  Further  Analysis  of  the  Motion  of  the  Pendulum : 
Simple  Harmonic  Motion.  —  The  motion  of  the  pendulum 
follows  very  closely  indeed  the  law  of  what  is  known  as 
simple  harmonic  motion. 

This  is  the  motion  which  a  point  a,  traveling  back  and 
forth  along  the  diameter  of  a  circle  (Fig.  37),  would 
make,  were  it  to  follow  the  movement  of  a  point  b  upon 
the  periphery  in  such  a  manner  that  while  the  latter 
travels  on  the  circumference  with  a  uniform  speed,  the 
line  which  connects  it  with  a 
is  always  perpendicular  to  the 
diameter  cd. 

Evidently  the  speed  of  a  will 
be  variable,  rising  from  zero  at 
c,  and  at  d,  when  6,  which  con- 
trols its  motion,  is  traveling 
at  right  angles  to  cd,  and  reach- 
ing a  maximum  speed  when- 
ever it  passes  the  center  o,  at 
which  times  b  moves  parallel 
to  the  diameter  cd.1 

The  harmonic  motion  of  a  is  indeed  of  the  nature  of  an 
oscillation  or  vibration  about  the  position  of  equilibrium  o. 
Its  characteristics  are  those  of  the  motions  of  the  pendu- 
lum, the  tuning  fork,  etc. 

1  Simple  harmonic  motion  may  be  defined  as  '*  the  projection  upon  a 
fixed  line  of  uniform  motion  in  a  circle"  (Elements  of  Physics,  Vol.  I, 
p.  46).  The  speed  of  a  in  terms  of  b  may  be  expressed  by  means  of  the 

equation 

.  v&  =  vb  sin  a, 

where  va  is  the  speed  of  a,  vb  the  linear  speed  of  &,  and  a  is  the  angle 
which  the  radius  bo  makes  with  cd.     (Fig.  37.) 

The  position  of  a  with  reference  to  o  is  given  by  the  equation 

x  —  r  cos  a, 
where  ao  is  the  distance  required,  and  r  is  the  radius  of  the  circle. 


54 


THE   OUTLINES   OF  PHYSICS 


47.  The  Curve   of   Sines.  —  If  we  imagine  the  paper  in 
Fig.  37  moved   uniformly  along  under  the  circle  and  at 

right  angles  to  the  diameter  c  d,  and 
the  point  a  capable  of  tracing  its 
course  upon  the  paper,  the  result  will 
be  a  curve  characteristic  of  simple 
harmonic  motion.  This  curve,  which 
is  called  the  curve  of  sines,  is  given  in 
Fig.  38.  It  describes  very  completely 
such  a  motion  as  that  of  a  pendulum. 
Times,  for  example,  are  measured 
along  the  line  OY.  The  intervals 
y$v  &&&  y$v  etc-'  correspond  to 
the  single  period  of  oscillation,  while 
the  intervals  y^  y6,  etc.,  mark  the 
double  or  complete  period. 

Lines  like  y±  in,  y§  q,  etc.,  drawn  at  right  angles  from 
OY  to  the  crest  of  the  curve,  measure  the  amplitude, 
while  a  line  p  n,  drawn  from  a  point  p  to  the  curve,  gives 
the  position  of  the  pendulum  with  reference  to  its  position 
of  equilibrium  at  any  time  t,  which  the  point  p  represents. 

48.  The  Tracing  of  a  Sine  Curve  by  Means  of  a  Pendulum. 
-  That  the  motion  of  a  pendulum  is  in  fact  of  the  char- 
acter just  described,  may  be  shown  as  follows : 

A  pendulum  is  mounted  so  as  to  swing  transversely 
above  a  plate  of  smoked  glass  (Fig.  39).  The  bob  of  the 
pendulum  must  have  a  vertical  hole,  coincident  with  its 
axis,  within  which  plays  a  stylus.  »(See  Fig.  40.) 

The  experiment  consists  in  placing  the  plate  beneath 
the  pendulum  in  such  a  position  that  the  stylus,  when  at 
rest,  touches  the  smoked  surface  near  the  middle  of  the 
shorter  edge.  The  longer  diameter  of  the  plate  must  lie 


THE  PHYSICAL  PENDULUM 


55 


at  right  angles  to  the  plane  of  vibration  of  the  pendulum. 
The  pendulum  is  now  given  an  amplitude  of  about  5  cm., 


FIG.  40. 


FIG.  39. 

and  after  it  has  completed  a  few  excursions,  the  plate  is 
drawn  under  it  with  as  steady  a  motion  as  possible.  The 
path  of  the  stylus  will  be  found  to  consist  of  a  curve  vary- 
ing from  the  curve  of  sines  only  in  so  far  as  the  motion  of 
the  plate  varies  from  uniformity  of  direction  or  speed. 

49.  The  Measurement  of  Gravitation.  —  The  first  direct 
experimental  evidence  that  the  earth's  attractive  force 
differs  on  different  parts  of  the  surface  of  the  planet, 
appears  to  be  due  to  the  astronomer  Richer,  who  in  1672 
took  a  clock  from  Paris  to  Cayenne  for  the  purpose  of 
certain  observations.  He  found  that  the  timepiece  lost 
about  2J-  minutes  daily  in  its  new  locality.  The  pendu- 
lum was  shortened  sufficiently  to  restore  it  to  its  normal 


56 


THE   OUTLINES   OF  PHYSICS 


rate,  and  when  later  it  was  brought  back  to  Paris  it  was 
found  to  be  gaining  2|-  minutes.1 

This  result,  which  is  quite  in  accordance  with  our  con- 
ception of  the  nature  of  gravitation  and  our  knowledge 
of  the  shape  of  the  earth,  has  since  been  verified  by  deter- 
minations of  the  value  of  g  in  various  parts  of  the  world. 

For  the  measurement  of  gravitation  the  pendulum  is 
by  far  the  most  accurate  instrument.     By  the  method  of 
coincidences   the    period   of   oscillation  can  be 
found  with  extraordinary  precision.    The  deter- 
mination of  the  corrected  length  (7)  with  a  cor- 
responding degree  of  accuracy  is  a  more  difficult 
matter.     Originally  a  simple  pendulum  with  a 
heavy   spherical   bob  was   used.      Borda,  with 
such  an  instrument,  found .  the   length   of   the 
seconds  pendulum  in   Paris  to  be  99*332  cm., 
and  the  acceleration  due  to  gravitation  in  that 
place,  980-96  cm.     Later,  Captain  Kater  of  the 
British   Navy   (1818)  introduced   a   pendulum 
based  upon  the  principle  of  the  interchangea- 
bility  of  the  centers  of  suspension  and  oscilla- 
tion.2     This   instrument,    which   is   called   the 
reversion  pendulum,  has  two  sets  of  adjustable 
knife-edges.      These   are  so   placed  that  when 
the  pendulum   swings   from   one    of   them,  aa 
(Fig.  41),  the  other,  bb,  is  as  nearly  as  may  be  at  the 
center  of  oscillation.     The  rate  in   this  position  having 
been  found,  the  instrument  is  suspended  from  bb.     Any 
change   in   rate   indicates   that    bb    requires    adjustment. 
When,    finally,    the    pendulum    swings    with    the    same 

1  Lommel,  Experimental  Physik,  p.  71. 

2  For  the  demonstration  of  this  principle,  which  was  discovered  by  the 
Dutch  physicist  Huygens  (1673),  see  Elements  of  Physics,  p.  75. 


FIG.  41. 


THE  PHYSICAL   PENDULUM 


57 


period  in  both   positions,  the    distance    aa   to   bb   is    the 
length  (Z).     All  the  quantities  in  the  formula 


are  then  known,  excepting  g. 

The  figure  shows  in  cross-section  a  standard  form  of 
the  reversible  pendulum.  It  is  designed  to  give  complete 
symmetry  of  outward  form,  with  the  concentration  of  mass 
chiefly  in  one  end. 

By  means  of  such  pendulums,  precise  determinations  of 
gravity  have  been  made  in  many  parts  of  the  world.  In  the 
following  table  are  given  some  of  the  values  thus  obtained. 

TABLE   I. 
VALUES  OF  THE  ACCELERATION  DUE  TO  GRAVITATION. 


Locality. 

Latitude. 

Elevation 
above  the  sea. 

Value  of  G. 
(not  reduced  to 
sea-level). 

Boston,  Mass.  .     .     . 

42°  21'  33" 

22  meters 

980-382  cm. 

Philadelphia,  Pa.      . 

39°  57'  06" 

16        " 

980-182    " 

Washington,  D.C.    . 

38°  53'  20" 

10        " 

980-100    " 

Cleveland,  O.  .    .    . 

41°  30'  22" 

210        " 

980-227    " 

Cincinnati,  O.  .     .     . 

39°  08'  20" 

245       " 

979-990    " 

Chicago,  111.     .    .    . 

41°  47'  25" 

182        " 

980-264    " 

St.  Louis,  Mo.      .     . 

38°  38'  03" 

154        » 

979-987    " 

Kansas  City,  Mo.     . 

39°  05'  50" 

278        " 

979-976    " 

Denver,  Col.    .     .     . 

39°  40'  36" 

1638 

979-595    " 

San  Francisco,  Cal.  . 

37°  47'  00" 

114        " 

979-951    " 

Greenwich  .... 
Paris 

51°  29'  00" 
48°  50'  11" 

47        " 

72        " 

981-170    " 
980-960    " 

Berlin      . 

52°  30'  16" 

35        " 

981-240    " 

Vienna    . 

48°  12'  35" 

150        " 

980-852    u 

Rome  

41°  53'  53" 

53        " 

980-312    " 

Hammerfest     .     .     . 

70°  40'  00" 

982-580    " 

58 


THE  OUTLINES   OF  PHYSICS 


CHAPTER   VII 
KINETIC  ENERGY;   POTENTIAL  ENERGY;   WORK 

50.  Work.  —  The  study  of  the  motion  of  the  pendulum 
leads  us  to  a  very  important  topic  : 
that  of  energy.  When  we  wish  to 
start  a  pendulum  into  oscillation, 
we  first  lift  the  bob  from  its  posi- 
tion of  rest  a  (Fig.  42),  into  a 
new  position  £>,  causing  it  to  follow 
the  circular  path  in  which  the 
pendulum  is  constrained  to  move. 
In  the  language  of  physics,  when 
l  a  body  is  moved  from  one  position 
FlG>  42.  to  another  against  any  force,  work 

is  done  upon  it. 


51.  Work;  how  measured.  —  Work  is  measured  by  the 
product  of  the  force  against  which  the  motion  takes  place 
and  the  distance  through  which  the  body  moves  against  it. 

In  this  case  the  force  is  gravitation,  and  if  the  bob  of 
the  pendulum  have  a  mass  m,  the  force  of  gravitation  act- 
ing upon  it  is  mg. 

It  cannot  be  said,  however,  that  the  bob  has  been  moved 
along  the  whole  path  ab  in  opposition  to  gravitation.  We 
must  resolve  the  path  ab  into  two  components,  ac  (hori- 
zontal), and  be  (vertical).  To  the  movement  along  ac, 
gravitation  offers  no  opposition,  and  no  work  against  that 


C  I 


ENERGY  59 

force  need  be  done ;  along  the  vertical  component  be,  how- 
ever, work  must  be  done,  and  it  is  this  vertical  component 
only  which  we  have  to  consider.  The  work  in  the  case  of 
the  pendulum  may,  therefore,  be  expressed  by  the  equation 

W=mgs, 

where  m  is  the  mass  of  the  bob,  g  the  acceleration  due  to 
gravitation,  and  s  the  vertical  component  (be)  of  the  dis- 
tance through  which  it  has  been  moved. 

52.  Energy;  Kinetic  and  Potential. — Suppose  the  pendu- 
lum bob,  at  b,  to  be  released.  It  will  soon  regain  its 
former  level,  but  in  so  doing  it  will  acquire  velocity. 
Because  of  its  velocity  it  will  possess  what  is  called 
energy  of  motion  or  kinetic  energy. 

In  the  case  of  the  pendulum,  the  bob  is  not  free  to  fall 
vertically  along  the  path  be,  but  in  following  the  circular 
path  from  b  to  a  it  acquires  precisely  the  same  velocity 
and  the  same  amount  of  kinetic  energy. 

This  energy  it  is  which  enables  the  bob  to  rise  against 
gravitation  on  'the  other  side  of  its  position  of  equilibrium. 
As  it  rises  towards  the  turning  point  it  loses  velocity  and, 
consequently,  kinetic  energy.  What  is  lost  in  kinetic 
energy  is,  however,  gained  in  energy  of  another  kind :  a 
sort  of  latent  or  stored  energy  due  to  the  position  of  the 
bob  at  higher  and  higher  levels. 

When  the  turning  point  is  reached,  the  kinetic  energy 
has  disappeared.  The  pendulum  is  at  rest.  It  is  not  in 
the  condition  in  which  it  was  at  the  beginning  of  the 
experiment,  however ;  it  is  in  the  condition  which  it  was 
after  work  had  been  done  upon  it  to  raise  it  to  the 
position  b.1 

1  Losses  due  to  atmospheric  resistance  and  to  the  existence  of  other 
forces  than  that  of  gravitation  are  not  taken  into  account. 


60  THE   OUTLINES   OF  PHYSICS 

The  energy  of  position  thus  gained  is  called  potential 
energy.  Potential  energy  may  be  stored  in  bodies  in  a 
variety  of  ways  other  than  that  of  lifting  them  from  a 
lower  to  a  higher  level.  Whenever  a  body  is  forced  into 
a  strained  position,  as  when  a  spiral  spring  is  stretched  or 
compressed,  or  a  bow  is  bent,  or  even  when  the  parts  of  a 
body  are  placed  in  unstable  atomic  or  molecular  relations 
to  each  other,  as  in  the  case  of  gunpowder  and  other  ex- 
plosives, the  body  is  imbued  with  potential  energy.  Such 
forms  of  potential  energy,  to  distinguish  them  from  the 
energy  of  mere  position,  are  called  potential  energy  of 
configuration. 

Kinetic  energy  is  conveniently  measured  by  means  of 
the  mass  and  the  velocity  which  it  possesses.  It  is,  how- 
ever, as  has  been  demonstrated  by  countless  careful  experi- 
ments, the  precise  equivalent  of  the  work  previously  done 
in  raising  the  bob  to  its  position  b. 

This  work  is  mgs.  The  quantity  $  is,  however,  J  v, 
where  v  is  the  velocity  after  the  bob  has  fallen  to  c. 
(See  Arts.  25  and  26.)  The  quantity  g,  moreover,  is 
itself  equivalent  to  v,  so  that  the  kinetic  energy  which 
is  equal  to  the  wrork  W  may  be  expressed  thus : 

E  —\  mv*  —  mgs  =  W. 

53.  The  Erg.  —  The  unit  of  energy  and  of  work  is  the 
erg.  It  is  the  work  done  by  a  force  of  one  dyne  acting 
through  a  distance  of  one  centimeter.  This  is  a  very  small 
quantity  of  work  indeed.  The  earth  exerts  a  force  of 
from  980  to  981  dynes  upon  each  grain  of  matter  at  its 
surface;  and  the  definition  of  the  erg  refers,  therefore, 
to  the  work  of  lifting  a  gram  one  centimeter  against  a 
force  scarcely  more  than  a  thousandth  as  great  as  gravi- 
tation. 


ENERGY  61 

The  Foot-Pound. —  Engineers  who  use  British  unit% 
employ,  as  the  unit  of  work,  the  work  necessary  to  raise 
a  pound  weight  avoirdupois  one  foot.  This  is  called 
the  foot-pound.  Where  metric  systems  prevail,  the  cor- 
responding practical  unit  is  the  kilogram-meter. 

In  localities  where  g  =  980.5,  the  foot-pound  is  13,560,- 
000  ergs  and  the  kilogram-meter  is  98,050,000  ergs. 

54.  Energy  of  the  Pendulum.  —  In  attempting  to  express 
the  energy  of  a  physical  pendulum,  in  terms  of  the  mass 
and  the  velocity,  the   difficulty  arises  that  the    different 
particles  of  which  the  pendulum  is  composed  are  situated 
at  various  distances  from  the  axis  of  suspension,  and  con- 
sequently possess  different  linear  velocities. 

We  may  regard  the  pendulum  as  made  up  of  an  infinite 
number  of  simple  pendulums,  all  bound  rigidly  together 
and  oscillating  with  a  common -period  (that,  namely,  of 
the  simple  pendulum,  the  mass  of  which  lies  in  the  center 
of  oscillation). 

While  these  simple  pendulums  vary  as  to  linear  velocity, 
they  all  swing  through  a  given  angle  in  the  same  time. 
The  motion  of  a  rotating  body,  or  of  a  body  oscillating 
about  a  fixed  axis,  can  be  expressed  more  conveniently  by 
means  of  its  rate  of  angular  motion  than  by  the  various 
linear  motions  of  its  parts. 

55.  Angular   Velocity.  —  The   rate  of  rotary  motion   is 
expressed  by  means  of  the  term  angular   velocity,  which 
is  the  rate  of  rotation.     For  the  uniform  motion  of  rotation 
the  angular  velocity  is  simply  the  angle   (in   radians)1 

1  Radian :  the  angle  which  incloses  an  arc,  the  length  of  which  is  equal 
to  the  radius  of  the  circle  to  which  the  arc  belongs.  Since  there  are  in  an 
entire  circumference  2  IT  radians,  a  body  revolving  uniformly  at  the  rate 
of  n  revolutions  per  second  possesses  an  angular  velocity  w  =  2  irn. 


62  THE  OUTLINES   OF  PHYSICS 

passed  through  in  one  second.  In  the  case  of  variable 
rotary  motion  or  of  oscillations,  we  may  conceive  the  body, 
at  the  instant  for  which  the  velocity  is  required,  to  be 
released  from  the  action  of  all  forces  except  those  which 
compel  its  particles  to  follow  their  circular  paths.  The 
angle  in  radians  through  which  it  would  then  move 
(uniformly)  in  one  second  measures  its  velocity  at  the 
instant  in  question. 

56.  Moment  of  Inertia,  —  The  energy  of  a  rotating  or 
oscillating  body  is  proportional  to  the  square  of  its  angular 
velocity  (G>),  just  as  that  of  a  body  possessing  motion  of 
translation  is  proportional  to  the  square  of  its  linear 
velocity.  To  obtain  the  amount  of  energy  in  the  former 
case,  however,  we  must  not  multiply  o>2  by  J  m,  but  by 
another  quantity,  ^K,  which  depends  not  only  upon  the 
mass,  but  likewise  upon  the  distribution  of  the  mass 
around  the  axis  of  rotation  or  of  suspension.  The  quan- 
tity /fin  the  equation 


which  gives  the  kinetic  energy  of  a  rotating  body,  is 
called  the  moment  of  inertia  of  the  body  about  its  axis  of 
revolution. 

That  K  must  depend  upon  the  distance  of  the  mass 
from  the  axis  of  rotation,  as  well  as  upon  the  mass  itself, 
is  obvious.  Consider,  for  example,  the  case  of  two  wheels, 
each  of  which  weighs  10  kilograms.  One  of  them  has  its 
mass  chiefly  in  a  rim,  at  a  radius  of  60  cm.  from  the  axis, 
the  other  an  equally  large  amount  of  matter  in  a  rim  with 
a  radius  of  20  c.  To  put  these  two  wheels  into  revolution 
at  the  rate  of  1  turn  per  second  (o>  =  2  TT  =  6.283),  will 
take  very  different  amounts  of  work,  although  the  masses 
are  the  same  and  the  angular  velocities  are  the  same. 


ENERGY  63 

In  the  large  wheel  the  matter  in  the  rim  will  be  travel^ 
ing  about  360  cms.  per  second,  in  the  small  wheel  only 
about  120  cm.  Their  kinetic  energies,  if  we  may  neglect 
the  masses  of  hubs  and  spokes,  will  be  about  as  9:1. 
The  large  wheel  in  coining  to  rest  will  do  about  nine 
times  as  much  work. 

57.    EXPERIMENT  11.  —  Energy  stored  in  a  Fly  Wheel. 

Apparatus : 

(1)  Thirty  or  forty  kilograms  of  the  iron  disk  weights  described  in 
Appendix  III,  one  of  them  provided  with  a  hook.     Weights  of  10  kg. 
each  are  to  be  preferred. 

(2)  An  iron  wheel  and  axle.     The  wheel  should  be  at  least  25  cm. 
radius,  and  rather  light.     The  driving-wheel  of  an  ordinary  sewing 
machine  is  a  good  pattern. 

The  wheel  should  be  mounted  upon  an  axle  not  less  than  50  cm.  in 
length.  A  keyed  shaft  of  steel  is  the  best.  The  wheel  should  be  near 
one  end  of  the  shaft.  The  shaft  must  have  substantial  bearings  of 
wood  or  metal  in  which  it  runs  smoothly.  It  is  important  that  the 
wheel  be  well  balanced  and  the  shaft  straight. 

(3)  Five  or  six  meters  of  stout  cotton  rope  from  0-5  cm.  to  0-8  cm. 
in  diameter.      This   should  be  soft,  pliable,  and  capable  of  much 
stretching  without  rupture.     It  must  be  strong   enough  to  sustain 
several  times  the  weight  employed  in  the  experiment. 

Procedure : 

(a)  The  wheel  is  mounted  between  two  strong  tables  to  which  the 
bearings  are  firmly  clamped  (see  Fig.  43).  The  weights  are  placed 
upon  the  floor  directly  below  the  longer  arm  of  the  shaft.  One  end 
of  the  rope  is  tied  around  a  spoke  of  the  wheel,  the  other  to  the  hook 
of  the  weights. 

(6)  The  operator  turns  the  wheel  from  him  with  one  hand,  guiding 
the  rope  so  as  to  wind  it  snugly  upon  the  shaft  until  all  the  slack  is 
taken  up.  He  then  draws  upon  the  rope  with  a  steady  but  increasing 
motion,  thus  setting  the  wheel  into  briskly  accelerated  revolution. 
When  the  rope  is  all  unwound,  the  wheel,  now  at  high  speed,  begins 
to  rewind  it  in  the  opposite  sense.  The  operator  still  holds  the  slack 
of  the  rope,  giving  sufficient  tension  to  secure  a  snug,  smooth  wind- 


64 


THE   OUTLINES   OF  PHYSICS 


ing.  Just  before  the  last  of  the  slack  is  taken  up  he  releases  the  rope. 
The  wheel,  still  running  with  a  considerable  velocity,  will  be  seen  to 
raise  the  heavy  weights,  perhaps  fifteen  or  twenty  times  its  own  mass, 
bodily  from  the  floor  and  to  a  height  of  many  centimeters. 


FIG.  43: 


58.  The  Conservation  of  Energy,  —  In  these  changes,  as 
regards  energy,  which  the  bob  of  a  pendulum  undergoes 
in  the  course  of  its  oscillation,  we  have  one  of  the  simplest 
examples  of  what  is  called  the  transformation  of  energy. 
Energy  changes  continually  from  the  kinetic  to  the  poten- 
tial form,  and  vice  versa,  and  it  is  transferred  from  one  body 
to  another;  but  it  can  neither  be  created  nor  destroyed. 
This  fact  is  expressed  in  what  is  known  as  the  law  of  the 
conservation  of  energy,  which  may  be  stated  thus : 

The  sum  of  the  potential  and  kinetic  energy  of  a  body 
always  remains  constant  excepting  as  the  body  may  receive 
energy  by  the  action  upon  it  of  forces  from  without  (viz. 
forces  due  to  the  action  of  other  bodies  upon  it),  or  as  it 
may  give  up  energy  to  other  bodies  by  doing  work  upon  them. 

Left  to  itself,  in  other  words,  a  body  or  system  of  bodies 
never  gains  or  loses  energy.  If  its  amount  of  energy  is 
increased,  it  is  at  the  expense  of  the  energy  of  other  neigh- 
boring bodies.  If  it  loses  energy,  neighboring  bodies  gain 
a  like  amount.  The  sum  total  of  energy  in  the  universe 
is  constant,  but  it  is  transferred  from  body  to  body  and 
is  transformed  continually. 


MACHINES 


65 


CHAPTER  VIII 

MACHINES 

59.  A  machine,  in  mechanics,  is  a  device  for  the  advan- 
tageous application  of  force. 

Simple  machines  are  those  in  which  a  single  device  is 
used.     The  most  important  of  these  are : 
The  pulley. 

The  lever  in  its  various  forms. 
The  inclined  plane  and  its  modifications. 

60.  The  Pulley.  —  A  single  pulley  (Fig.  44)  is  simply 
a  device  for  changing  the  direction  of  a  force.     It  is  a  form 
of  the  lever  with  equal  arms, 

as  will  be  seen  when  that  de- 
vice is  considered  (Art.  61). 
By  the  combination  of  pul- 
leys, however,  the  principle 
of  work  is  introduced,  and 
large  forces  are  obtained  by 
the  intelligent  application  of 
a  small  one.  Figure  45  shows 
the  simplest  case  ;  that  of  one 
fixed  pulley  A,  and  a  mov- 
able  one  B. 

The  effect  of  this  combination  may  be  gathered  from 
the  following  considerations : 


66 


THE  OUTLINES   OF  PHYSICS 


(1)  The  stress  upon  the  rope  must  be  everywhere  the 
same ;  consequently  the  downward  force  at  P2,  necessary 

c — v      to    produce     equilibrium,    must    be 

<- TT -r ^     twice  as  great  as  that  at  Pr     (The 

/TH  A      "'  latter  force  is  balanced  by  the  stress 

upon  the  rope ;  the  former,  by  twice 
that  stress,  i.e.  by  the  stress  in  th< 
branch  b  +  the  stress  in  the  branch  <?.) 

(2)  Since  the  rope  remains  taut, 
every  vertical  movement  of  P1  will 

Q^      >i  be  accompanied  by  one  half  as  great 

M  )„  a  movement  of  P2. 

(3)  The  force   of  the  earth  upon 
Pl  is  mg  where  m  is  the  mass  of  Pv 
so  that  the  body  at  P2   (including 
the  pulley)  must  have  a  mass  2  m, 
which  will   exert  under   the    action 

of  the  earth  a  force  2mg,  or  twice  that  at  Pr 

(4)  The  work  done  by  P1  in  falling  n  centimeters  is 

mgn.     The  work  done  upon  P2  to  raise  it  -  centimeters 

2 

is  2  mg  x  -  =  mgn. 

This  simple  method  of  reasoning  will  serve  in  the  analy- 
sis of  any  problem  dealing  with  systems  of  pulleys. 

It  will  be  seen  from  the  above  that  there  is  no  saving 
of  work  by  this  device,  a  statement  which  is  true  of  all 
machines,  however  complicated  they  may  be.  On  the  other 
hand,  there  are  losses  due  to  friction,  etc.,  of  which 
no  account  has  been  taken,  and  these  losses  sometimes 
consume  a  considerable  proportion  of  the  work  done. 


61.   The  Lever.  —  In  its  simplest  form   the   lever   is   a 
rigid  bar  supported  at  a  point  (Figs.  46  and  47)  called 


MACHINES 


67 


the  fulcrum.  At  two  points,  a  and  5,  upon  the  bar,  forces 
acting  at  right  angles  to  its  axis  are  applied.  These  are 
opposed  to  each  other ;  that  is  to  say,  they  tend  to  produce 


=  20,000  dynes 


30,000  dynes 


FIG.  46. 


rotation  around  the  fulcrum  in  opposite  directions.  The 
distances  d^  and  d2  from  the  points  of  application,  a  and  b 
respectively,  to  the  fulcrum,  are  called  the  lever  arms. 


-.  -f-  25,000  dynes 


/2—    50,000  dynes 


FIG.  47. 

It  is  convenient  to  distinguish  two  classes  of  levers. 

(1)  Those  in  which  the  fulcrum  lies  between  the  points 
of  application. 

(2)  Those  in  which  the  points  of  application  are  both 
on  the  same  side  of  the  fulcrum. 

62.  The  Moment  of  a  Force  is  the  product  of  the  force 
into  its  distance  from  the  fulcrum. 

The  moment  of  the  force  fv  for  example,  the  point  of 
application  of  which  is  at  a,  is  f^\  that  of  /2  is  f2dr 


68  THE  OUTLINES   OF  PHYSICS 

63.  Law  of  the  Lever  (applicable  to  all  cases  of   both 
classes  and  to  all  combinations  of  levers). 

The  sum  of  the  moments  of  the  forces  must  be  equal  to 
zero. 

(In  the  above  statement  it  is  the  algebraic  sum  which 
is  referred  to ;  lever  arms  and  forces  being  counted  posi- 
tive or  negative  according  to  their  direction.) 

64.  EXAMPLE.  —  In  Fig.  46  let  lever  arms  to  the  right 
of  the  fulcrum  and  forces  acting  upwards  be  positive.    Let 
/!  be  30,000  dynes,  /2   20,000   dynes,  d1   20  cm.,  and  d2 
30  cm. 

The  moment  of  /j  is 

/^  =  -  30,000  x  -  20  -  +  600,000, 
and  the  moment  of  fz  is 

f^  =  -  20,000  x  +  30  =  -  600,000. 
Their  sum  is 

/A  +/A  =  o, 

which  is  the  equation  of  equilibrium. 
In  Fig.  47  we  may  assume 

c?!  =  —  50  cm., 
d2  =  —  25  cm. ; 
/!  =  +  25,000  dynes, 
/2  =  -  50,000  dynes. 
The  same  condition  will  be  fulfilled. 

65.  Case  of  a  Body  Free  to  revolve  upon  a  Fixed  Axis.  — 
The  principle  of  the  lever  may  be  extended  to  the  case 
of  a  body  of  any  shape  to  which  forces  are  applied,  pro- 
vided the  body  is  free  to  revolve  around  a  fixed  axis. 

The  straight  line  perpendicular  to  the  axis,  and  con- 
necting the  point  of  application  of  a  force  with  the  latter, 


MACHINES 


69 


is  the  lever  arm  of  that  force.  If  the  force  does  not  act 
at  right  angles  to  the  lever  arm,  only  its  component  per- 
pendicular to  the  arm  is  to  be  taken  in  finding  its  moment. 


FIG.  48. 

In  Fig.  48,  F  is  the  fulcrum,  or  axis  of  revolution.  At 
a  and  b  the  forces  of  /x  and  /2  are  applied.  The  former 
is  not  perpendicular  to  its  lever  arm  Fa. 

To  find  the  moment  of  fv  we  find  its  component  ok, 
perpendicular  to  the  arm,  and  take  the  product 

Fa  x  ak  =  moment. 

Another  and  simpler  method  is  to  drop  a  perpendicular  d^ 
to  the  force  /j  and  take  the  product 

d^  =  moment  of  /r 
The  result  is  the  same.1 

1  The  identity  of  the  two  methods  is  readily  shown. 
Since  ak  =  f\  cos  /3,  we  have 

Fa  x  ak  =  Fafi  cos  ft. 
Since  d\  —  Fa  cos  a,  we  have  likewise 

.  difi  -  Fafi  cos  a. 

The  triangles  Fac  and  akg,  however,  are  similar  and  a  is  equal  to  ft  ; 
•'•  dii  =  Fa  x  ak. 


70  THE  OUTLINES   OF  PHYSICS 

66.   The  Principle  of  Work  applied  to  the  Lever.  —  The 

truth  of  the  statement  already  made  with  reference  to  all 
machines,  that  no  work  is  gained,  is  obvious  in  the  case 
of  the  lever. 

a  so 


__,----       /  \  10 


FIG.  49. 

Let  the  weights  m  and  5  m  be  balanced  upon  a  bar  ab 
(Fig.  49).  The  lever  arms  are  therefore  as  5:1. 

If  sufficient  additional  weight  be  added  at  a  to  overcome 
the  friction,  and  m  move  down  through  a  distance  equal 
to  ac,  the  weight  at  b  will  be  raised  vertically  through  the 
distance  be.  The  triangles  Fac  and  Fbe,  however,  are 
similar,  and 

ac  :  be  :  :  5  : 1. 

Let  the  distance  be  be  1  cm. 

The  force  at  a  is  mg  dynes,  the  distance  traversed  is 
5  cm.,  and  the  work 

W=  5mg  ergs. 

The  work  done  upon  the  weight  at  b  is  the  product  of 
1  cm.  and  5  mg  dynes,  which  is  the  precise  equivalent 
of  the  above. 

67.  The  Pulley  and  the  Wheel  and  Axle  considered  as 
Levers.  —  The  ordinary  lever  is  of  advantage  where  forces 
are  to  be  balanced  against  one  another,  or  for  small  move- 
ments, rather  than  for  the  movement  of  masses  through 
considerable  distances.  As  the  lever  arms  are  turned  the 


MACHINES 


71 


moments  of  the  forces  change.  Thus  in  Fig.  50  the 
moments  of/j  and/2  are  aF  •  f^  and  bF  -/2  when  the  arms 
are  horizontal.  When  turned  into  the  position  a^bv  how- 
ever, these  are  reduced  to  d^f^  and  c?2/2. 


FIG.  50. 


The  pulley  is  a  form  of  lever  in  which  this  defect  is 
remedied.  The  effective  lever  arms  d±  and  d2  (Figs.  51 
and  52)  are  radii  of  the  wheel  drawn  to  the  points  upon 


FIG.  51. 


FIG.  52. 


72 


THE  OUTLINES   OF  PHYSICS 


the  periphery  at  which  the  rope  leaves  the  pulley.  These 
arms  are  of  unvarying  length,  however  great  the  move- 
ment may  be. 

The  common   pulley  is  a  lever  with   equal   arms ;  the 
wheel  and  axle  (Fig.  53),  however,  combines  the  advan- 
tages  of    constant  moments   and 
of  unequal  arms. 

68.   The  Inclined  Plane.  —  The 
inclined  plane  and   its  modifica- 
tions, the  screw  and  the  wedge, 
present  a  slightly  different  method 
of   overcoming  a  large  force  by 
means  of   a   smaller    one   which 
acts   through   a   correspondingly 
greater  distance. 
Suppose  it  to  be  required  to  raise  the  ball  B  (Fig.  54), 
which  rests  upon  a  horizontal  surface,  through  a  vertical 
distance  n. 

The  work  required  is  n  mg,  where  m  is  the  mass  of  B. 
Along  the  vertical  path  the  force  would  be  mg,  but  by  roll- 


FIG.  53. 


FIG.  54. 


ing  the  ball  along  an  inclined  plane  of  proper  pitch,  any 
given  smaller  force  /  may  be  made  to  carry  it  to  the  re- 
quired height.  The  work  expended  is  the  same  as  before, 
plus  that  necessary  to  overcome  friction. 


MACHINES 


73 


To  find  the  force  necessary  to  carry  the  ball  up  a  given 
plane  cib,  suppose  it  placed  upon  the  plane,  and  the  force 
mg  with  which  the  earth  attracts  it  resolved  into  two 
components.  Of  these  p  is  perpendicular  to  the  plane  and 
produces  pressure,  but  no  motion,  while  /,  parallel  to  the 
plane,  is  the  required  force.1 

The  work  done  by  /is 

fxab  =  n  mg. 

It  is  the  precise  equivalent  of  that  required  to  lift  the  ball 
vertically. 

69.   The  Relation  of  the  Screw  to  the  Inclined  Plane  may 

be  shown  by  rolling  a  triangular  strip  of  paper  aof  (Fig.  55) 
about  a  cylinder.     The  diagram  needs  no  elucidation. 


FIG.  55. 


Figure  56  shows  two  well-known  forms  of  screw  threads 
and  half  of  a  nut  or  screw-bearing  in  which  the  screw 
plays ;  the  latter,  when  fixed,  takes  up  the  thrust  or  reac- 
tion of  the  axial  motion  of  the  screw. 


FIG.  56. 

1  Since  the  triangle  of  forces  is  similar  to  abc  (Fig.  54),  the  value  of  /is 

f=mg  sin  a 
where  a  is  the  angle  which  measures  the  pitch  of  the  plane. 


74  THE  OUTLINES   OF  PHYSICS 

The  following  are  some  of  the  chief  advantages  of  the 
screw : 

(1)  It   may  be  given  a  motion  of   translation,  in  the 
direction  of  its  axis,  by  the  application  of  a  rotary  motion. 
The  action  of  the  screw  may,  therefore,  readily  be  made 
continuous,  which  is  a  great  advantage  in  any  mechanical 
device. 

(2)  It  is  a  form  to  which  great  strength  is  easily  given, 
so  that  by  the  use  of  a  long  lever  arm  an  enormous  force 
can  be  exerted  in  the  direction  of  the  screw  axis.1 

1  The  screw  affords  a  good  example  of  the  law  of  reaction  (third  law  of 
motion)  and  of  the  nature  of  force  considered  as  a  stress.  The  backward 
thrust  upon  the  nut  of  a  screw,  which  is  exerting  pressure  in  the  direc- 
tion of  its  axis,  is  precisely  equal  in  amount  to  the  pressure  exerted  and 
opposite  in  direction. 


THE  BALANCE  75 


CHAPTER   IX 

THE    BALANCE 

70.  Forces  in  Equilibrium,  —  Bodies  near  the  surface  of 
the  earth,  or  indeed  in  proximity  to  matter  of  any  kind, 
are  continually  acted  upon  by  forces.     When  a  body  is  at 
rest,  it  is  because  the  forces  acting  upon  it  are  balanced 
against  each  other. 

71.  Conditions  of  Equilibrium.  —  (1)  Case  of  a  body  free 
to   revolve  about   a   point  or  an  axis  of   rotation.     The 
condition  of  equilibrium  is  that  stated  in  a  previous  sec- 
tion, viz.  the  sum  of  the  moments  of  the  forces  must  be 
zero.    (2)  Case  of  a  body  sustained  in  any  manner  against 
the  attraction  of  the  earth  (or  against  any  parallel  forces). 
The   forces  may  be  regarded   as  supplanted   by  a  single 
force  (mg~)  acting  at  the  center  of  mass  (sometimes  called 
the  center  of  gravity). 

In  regular  homogeneous  solids,  the  center  of  mass  is  the 
geometrical  center  of  the  body.  (The  method  of  deter- 
mining the  position  of  the  center  of  mass  of  any  irregular 
body  is  given  in  Art.  74.) 

72.  Stability.  —  It  is  usual  to   describe   equilibrium  as 
STABLE  when  any  motion  to  which  the  body  can  be  sub- 
jected, without  change  of  the  level  of  -the  support,  will 
raise  the  center  of  mass ;  as  INDIFFERENT  when  such  mo- 
tions will  neither  raise  nor  lower  the  center  of  mass  ;  and  as 
UNSTABLE  when  such  motions  will  lower  the  center  of  mass. 


76 


THE   OUTLINES   OF  PHYSICS 


73.  Examples.  —  (a)  Point  of  support  above  the  center  of 
mass.  Equilibrium  will  be  had  only  when  the  center  of 
mass  is  vertically  below  the  point  or  axis  of  support.  The 
only  motion  of  which  the  body  is  capable  is  that  of  revo- 
lution, and  the  center  of  mass  will  rise  (see  Fig.  57).  If 
the  body  be  turned  from  its  position  of  equilibrium,  as 
shown  in  the  figure,  the  force  mg  acting  upon  the  center 
of  mass  will  always  have  a  component  tending  to  restore 
it  to  that  position. 


•i 

\ 

f 

\ 

^ 

\ 

\ 

\ 

\ 

\ 

\ 

v 

-' 

^      \ 

••-"*" 

\      . 

m 

\ 

wife    \ 

\     \      x 

o  \ 

^^          > 

V*      \           _.' 

\s~ 

^\ 

^'       \ 

f 

<         \ 

\         \ 

\    \ 

\           \ 

\ 

\ 

\ 

\ 

—  V"* 

^ 

\ 
\ 
\ 
\ 
\ 

\ 

\ 

x 

JL^L 

FIG.  57. 


FIG.  58. 


FIG.  59. 


(£)  Center  of  support  at  the  center  of  mass  (axis  of  sup- 
port passes  through  center  of  mass)  (Fig.  58).  The  body 
will  be  in  indifferent  equilibrium.  It  may  be  turned 
about  the  axis  at  will  without  raising  or  lowering  the 
center  of  mass.  It  has  no  tendency  to  return  to  any 
given  position. 

(c)  Support  below  the  center  of  mass.  If  the  support  be 
at  a  point  or  along  an  axis,  as  in  Fig.  59,  the  body  will  be 
in  unstable  equilibrium  when  the  center  of  mass  is  verti- 
cally above  the  support.  Any  movement  will  lower  the 
center  of  mass,  and  if  the  body  be  in  the  slightest  degree 
displaced  from  the  position  of  equilibrium,  the  force  mg 


THE  BALANCE  77 

will  have  an  active  component  which  tends  to  increase  the 
displacement. 

Stable  equilibrium  with  support  below  the  center  of 
mass  can  be  obtained  by  the  use  of  three  points  of 
support.  A  cylinder  lying  upon  its  side  (Fig.  60,  «) 
is  in  stable  equilibrium  as  regards  motion  in  the  direction 
of  its  axis,  and  in  indifferent  equilibrium  to  motions  at 
right  angles  to  its  axis.  If  it  be  flattened,  and  lie  with  its 


FIG.  60. 

major  diameter  horizontal  (5),  it  is  in  stable  equilibrium. 
If  the  major  axis  is  vertical  (<?),  there  will  be  stability  in 
the  axial  direction  and  instability  at  right  angles  to  the 
same. 

74.  EXPERIMENT  12.  —  To  find  the  center  of  mass  of  an  irregular 
solid. 

This  experiment  depends  upon  the  principle  stated  under  Example 
(a),  (Art.  73),  viz.  that  a  suspended  body  comes  into  stable  equilib- 
rium with  its  center  of  mass  vertically  below  the  center  of  support. 

Apparatus  : 

(1)  A  large  open  basket. 

(2)  A  plumb-line,  with  pointed  bob. 

(3)  The  pendulum  stand  described  in  Experiment  5. 

(4)  A  kilogram  weight,  some  strong  twine,  and  some  double  hooks 
of  wire ;  a  thread  and  needle. 

Procedure  : 

(a)  Suspend  the  basket  from  the  arm  of  the  pendulum  stand  by 
means  of  the  hook  and  twine,  in  any  position  such  that  the  line  of 


78 


THE  OUTLINES   OF  PHYSICS 


suspension,  continued,  would  pass  through  some  portion  of  the  basket 
mesh.  By  means  of  the  plumb-line,  which  is  to  be  suspended  from 
the  lower  branch  of  the  hook  which  holds  the  basket  (Fig.  Gl),  care 
being  taken  that  it  is  so  placed  as  to  form  the  continuation  of  the 
line  of  suspension,  determine  the  point  where  the  latter  penetrates 
the  mesh.  (This  can  be  quite  accurately  done  by  lowering  the  bob 
until  its  point  is  nearly  in  contact  with  the  wall  of  the  basket.) 

(J)  Mark   the  above   determined  point,   also   that   in  which    the 
plumb-line,  continued,  would  pierce  the  handle  of  the  basket  behind 


FIG.  61. 


FIG.  02. 


the  hook.  Take  the  basket  down,  and,  by  means  of  the  needle, 
stretch  a  thread  so  as  to  mark  the  position  which  the  vertical  line 
from  the  center  of  support  had  occupied,  i.e.  the  position  of  the 
plumb-line. 

(c)  Repeat  the  above  operation  with  the  basket  suspended  in  quite 
a  different  position  (Fig.  62).  If  the  two  trials  have  been  carefully 
made,  the  two  threads  will  cut  one  another,  or  very  nearly  so.  Since 
the  center  of  mass  lies  upon  both  threads,  it  must  be  located  at  their  inter- 
section. Note  that  the  center  of  mass  lies  at  a  point  not  occupied  by 
any  of  the  material  of  which  the  basket  is  composed. 

(d}  Fasten  the  weight  in  one  corner  of  the  basket  and  repeat  the 
experiment.  Note  that  the  center  of  mass  has  shifted. 


THE  BALANCE  79 

75.  The  Balance.  —  The  balance  is  a  lever  with  equal 
arms,  which  is  used  for  the  comparison  of  masses. 

Few  instruments  have  been  brought  to  a  higher  degree 
of  accuracy  and  delicacy.  With  a  good  balance,  for  ex- 
ample, it  is  possible  to  detect  with  certainty  differences 
between  two  masses  amounting  to  less  than  one  part  in  a 
million. 

Balances  of  precision  owe  their  delicacy  chiefly  to  the 
fact  that   the  center  of   mass   is  very 
near  the  axis  of  support.     If  m1  (Fig. 
63)  be  the  center  of  mass  of  a  balance        [  d 
which  oscillates  about  the  center  0,  and 
if  a  small  excess  of  weight  upon  the 
left-hand  pan  turn  the  beam  through  an 
angle  a,  the  entire  mass,  which  we  may 

consider  as  concentrated  at  the  center  mj*-^- '^ 

of  mass,  is  moved  to  nr     The  vertical  FlG- 63< 

distance  through  which  it  is  lifted   is  ^pv  with  an  ex- 
penditure of  work 

Wl  =  n\p\  X  mg. 


If  the  center  of  mass  is  at  w2,  nearer  to  0,  the  same  angle 
corresponds  to  a  displacement  of  m2  to  w2,  with  a  vertical 
rise  wt?  and  work 


The  work  in  the  two  cases,  to  which  the  sensitiveness  of 
the  balance  is  inversely  proportional,  is  in  the  ratio 

Wl  :  W%:  :  om^  :  om2. 

The  important  features  in  the  construction  of  the  balance 
are  indicated  in  Fig.  64. 

The  beam  is  made  of  a  single  piece  of  metal,  designed 
with  a  view  to  great  stiffness  and  to  minimum  of  mass. 


80 


THE  OUTLINES   OF  PHYSICS 


There  are  three  wedges,  technically  called  knife-edges :  a 
central  one  which  forms  the  axis  of  support,  and  one  at 
each  end,  upon  which  the  scale  pans  hang  freely  by  means 
of  stirrups.  The  knife-edges  are  accurately  ground,  and 
are  constructed  of  hardened  steel  or  sometimes  of  agate. 
They  rest  against  plane  bearings  of  agate.  The  three 
knife-edges  are  placed  in  the  same  horizontal  line,  and 


FIG.  64. 


this  line  is  located  just  above  the  center  of  mass.  A  long 
pointer,  which  swings  in  front  of  a  scale,  indicates  the  posi- 
tion of  the  beam.  A  short  upright  rod,  vertically  above 
the  knife-edges,  is  threaded  and  carries  a  milled  nut.  By 
raising  and  lowering  this  nut,  the  center  of  mass  can  be 
raised  and  lowered,  and  the  sensitiveness  of  the  balance 
changed. 

The  advantages  gained  by  this  method  of  construction 
are  as  follows : 

(1)  Since  the  scale  pans,  with  their  contents,  hang 
freely  from  the  knife-edges,  we  may  consider  their  masses 
as  concentrated  at  a  and  5,  and  since  these  points  are  at 
the  same  level  with  0  and  approximately  with  m  the 
center  of  mass,  the  balance  may  be  loaded  without  sensibly 
shifting  the  center  of  mass. 


THE  BALANCE  81 

(2)  By  the  use  of  knife-edges  two  points  are  gained : 
(a)   The  movements  of  the  beam  are  rendered  almost 

frictionless. 

(5)  The  lengths  of  the  arms  are  accurately  fixed  and 
are  rendered  unchangeable. 

The  latter  point  (5)  is  of  especial  importance,  because 
it  is  the  moments  of  the  forces  acting  at  a  and  b  that  are 
compared.  These  are  the  products 

Oa  x  ma  =  Ob  x  m^ 

where  ma  and  mb  are  the  masses  balanced  against  each 
other.  Now  Oa  and  Ob  must  be  strictly  unchangeable  and 
equal  (or  of  known  ratio),  in  order  that  we  may  deduce 
the  relation  of  the  masses  with  certainty. 

So  accurate  is  the  workmanship  of  the  best  balances, 
that  it  is  not  uncommon  to  find  that  the  arms  differ  in 
length  by  only  a  few  millionths. 

(3)  Sensitiveness  of  action  is  obtained  by  bringing  m 
and   0  as   near  together  as  it  is  possible  to  do  without 
losing  the  stability  of   equilibrium,  and  by  reducing  the 
mass  of   the  beam  to  a  minimum.     The   use    of   a   long 
pointer  makes  it  possible  to  detect  very  small  movements 
of  the  beam. 

76.  EXPERIMENT  13.  —  The  Balance.  Relation  between  Length  of 
Arm  and  Sensitiveness. 

Apparatus : 

(1)  A  wooden  strip  or  beam  60  cm.  long  and  3  cm.  x  1  cm.  in  cross- 
section  (Fig.  65).  Through  a  transverse  hole  in  the  same,  midway 
between  the  ends,  is  inserted  a  three-cornered  file  or  other  triangular 
bar  of  steel,  one  edge  of  which  is  to  serve  as  a  central  knife-edge  for 
support.  This  edge  is  perpendicular  to  the  principal  axis  of  the  beam, 
and  so  situated  that  when  the  latter  is  swinging,  its  center  of  mass 
will  be  just  below  the  support.  Along  the  axis  of  the  beam  are  bored 
G 


82 


THE  OUTLINES   OF  PHYSICS 


a  set  of  transverse  holes,  aL  «2,  &T  &2,  ct  e2,  ^  «72,  ^  e2,  each  about  2  mm. 
in  diameter.  These  are  situated  to  the  right  and  left  of  the  center  of 
mass,  at  distances  5  cm.,  10  cm.,  15  cm.,  20  cm.,  and  25  cm.,  respectively. 


FIG.  65. 

A  set  of  short,  straight,  metallic  rods  or  pins  are  fitted  within  these 
holes,  their  centers  lying  in  the  axis  of  the  beam. 

The  beam  hangs  from  a  stirrup  of  stiff  iron  wire,  of  the  form 
shown  in  Fig.  66.  Two  similar  stirrups 
support  the  weights  ml  m2  as  in  that 

/\r\  //        figure.     These   smaller  stirrups  must  be 

MM  //         adjusted  to  equal   one   another   in   mass 

|r          O byfiling- 

The  beam  is  provided  with  a  light 
stiff  pointer,  the  tip  of  which  is  vertically 
below  the  center  of  mass  when  the  beam 
is  horizontal.  The  pointer  moves  in 
front  of  a  circular  scale  with  equal  divi- 
sions. (Pointer  and  scale  may  be  con- 
structed of  cardboard.  The  former,  if 
of  metal,  must  be  as  light  as  is  consistent 
with  stiffness.) 

Under  each  of  the  weights  blocks 
should  be  piled  to  such  a  height  as  to 
limit  the  oscillations  of  the  beam  to  a 
small  arc. 


FIG.  66. 


THE  BALANCE  83 

It  will  be  seen  that  the  above  apparatus  approaches  in  a  simple 
manner  the  conditions  to  be  fulfilled  in  a  good  balance. 

The  various  supports  for  weights  av  a<2,  bv  &2>  etc->  are  in  a  straight 
line  passing  through  axis  of  support  of  the  beam,  and  the  latter  point 
is  near  the  center  of  mass. 

The  length  of  arm  can,  however,  be  varied  stepwise  from  Oal  to 
Oev  a  thing  not  readily  accomplished  with  ordinary  balances. 

Procedure : 

(a)  The  weights  mv  m2  (200  g.  each,  or  less  if  that  weight 
produces  appreciable  flexure  of  the  beam),  are  suspended  from  el 
and  e2.  Shot  are  added  to  the  lighter  side  until  the  pointer  oscillates 
through  nearly  the  same  range  on  both  sides  of  the  zero  of  the  scale. 

(&)  The  "position  of  rest"  of  the  pointer  is  found  by  the  method  of 
oscillations ;  that  is  to  say,  seven  successive  turning  points  are  noted, 
and  these  are  averaged. 

For  example,  when  the  observations  begin,  the  pointer  is  swinging 
to  the  left.  We  follow  it  with  the  eye  until  it  reaches  its  greatest 
elongation  and  starts  on  its  return  swing.  The  position  of  greatest 
elongation  is  noted;  also  the  six  following  ones  to  right  and  left 
alternately,  estimating  tenths  of  the  small  divisions.  The  readings 
are  to  be  tabulated  as  below. 

LEFT.  RIGHT. 

8-8 
7-9 
7-0 
6-2 
4)29-8 

7-475  av. 

Treating  the  quantities  on  the  left  side  as  negative  and  averaging, 
\\Q  find  the  position  of  the  zero  : 

9-000-  7-475  =  0.762+to  the  right. 

(c)  Taking  the  utmost  care  not  to  alter  in  any  way  the  relation  of 
the  parts  of  the  balance  to  one  another  by  touching  the  beam  or  even 
by  checking  the  oscillations,  as  any  such  disarrangement  tends  to 
shift  the  zero  point,  add  to  the  mass  on  one  side  a  small  weight  from 
the  box  of  weights  (1,  2,  or  5  eg.,  according  to  the  sensitiveness  of 


84  THE  OUTLINES   OF  PHYSICS 

the  balance),  sufficient  to  shift  the  zero  point  through  several  scale 
divisions.  Redetermine  the  zero  by  the  method  of  oscillations,  and 
divide  the  number  of  scale  divisions  through  which  it  has  been  dis- 
placed by  the  number  of  centigrams  added.  The  result  is  the  sensi- 
tiveness per  centigram.1 

(d)  Determine  the  sensitiveness,  per  centigram,  of  the  balance  with 
the  weights  at  dl  d2,  cl  c2,  ftj  J2,  and  aL  «2,  redetermining  the  zero  before 
adding  the  deflecting  weight  each  time.  Vary  the  deflecting  weight  in 
inverse  proportion  to  the  lever  arm. 

Express  the  results  obtained  graphically,  using  lengths  of  lever  arm 
as  abscissas,  and  sensitiveness  as  ordinates.  With  what  degree  of 
approximation  does  your  curve  agree  with  the  relation 

a:/, 

where  a  is  the  angle  of  displacement  due  to  one  centigram  and  I  the 
length  of  the  balance  arm  ? 

77.    EXPERIMENT  14.  —  Weighing  by  Substitution. 

Apparatus  : 

(1)  A  well  constructed  balance,  with  a  pointer  and  scale,  and  a  set 
of  weights. 

(2)  Two  evaporating  dishes  or  other  flat  open  vessels. 

(3)  About  500  g.  of  fine  shot. 

Procedure : 

(a)  Place  a  200  g.  weight  upon  the  right-hand  pan  of  the  balance, 
and  in  the  other  pan  one  of  the  dishes. 

(b)  Pour  shot  into  the  dish  until  the  pointer  remains  upon  the 
scale ;   then  read  seven  oscillations,  as  in  Experiment  13,  and  com- 
pute the  position  of  rest.     (Call  this  dish  of  shot  A.*), 

(c)  Remove  the  dish  with  its  load,  and  place  the  other  dish  upon 
the  pan.     Add  shot  until  the  point  reaches  the  same  position  of  rest, 
as  nearly  as  you  can  determine  it  without  taking  another  set  of  read- 
ings.    Whatever  the  value  of  the  weight  upon  the  other  pan,  and 
uihatever  the  ratio  of  the  arms  of  the  balance,  the  second  dish  of  shot, 
which  we  may  call  B,  is  of  the  same  weight  as  A,  within  the  limits 
of  accuracy  of  your  estimation  of  the  agreement  of  the  two  positions 
of  rest.     This  is  called  weighing  by  substitution. 

1  In  the  case  of  delicate  balances  the  sensitiveness  is  expressed  by  the 
displacement  per  milligram. 


THE  BALANCE  85 

(d)  To  estimate  the  accuracy  of  the  weighing,  obtain  the  position 
of  rest  with  dish  B  upon  the  pan,  employing  the  method  of  oscilla- 
tions. Subtract  the  same  from  the  position  of  rest  for  A.  Add  to 
one  pan  a  centigram  weight  (or  more  in  the  case  of  a  rough  balance), 
and  rede  term  ine  the  position  of  rest  by  oscillations. 

The  difference  between  the  positions  of  rest  for  A  and  B,  divided 
by  the  change  in  the  position  of  rest  produced  by  the  centigram 
weight,  gives  the  difference  in  weight  between  A  and  B  in  centi- 
grams. 

Example : 
With  dish  A : 

Seven  oscillations  gave  as  position  of  rest,  1-19  (left) 

With  dish  B : 

Seven  oscillations  gave,  O37  (left) 

Difference  =  0^82  s.  d. 

One  centigram  added  to  right-hand  pan  gave,  from  seven  oscilla- 
tions, 3-12  (right). 

The  influence  of  1  eg.  was  therefore 

3-12  +  -82  =  3-94  s.  d., 
and  the  difference  of  weight  between  A  and  .B  is 

—  eg.  =  0-0021  -  grams. 

0*94: 


86  THE   OUTLINES   OF  PHYSICS 


CHAPTER   X 

COHESION,   ADHESION,   AND  FRICTION 

78.  The  Molecular  Forces.  —  Friction,  adhesion,  cohe- 
sion, elasticity,  capillarity,  and  many  kindred  phenomena 
are  due  to  forces,  the  sphere  of  action  of  which  is  very 
small,  comparable  indeed  in  size  to  the  distances  which 
separate  the  molecules  of  a  solid  or  liquid. 

Such  forces  are  called  the  molecular  forces.  Their 
existence,  upon  which  the  stability  of  all  material  struc- 
tures depends,  may  be  demonstrated  in  a  variety  of  ways. 

If  a  piece  of  clean  dry  plate  glass  be  laid  upon  a  similar 
piece,  for  example,  we  find  upon  picking  it  up  again  that 
the  lower  piece  tends  to  follow.  The  nearer  we  succeed 
in  bringing  the  two  surfaces  to  one  another  the  stronger 
the  tendency  will  be.  Commonly  there  will  remain 
between  the  upper  and  lower  plates  a  considerable  layer 
or  cushion  of  air.  To  demonstrate  its  presence  we  have 
only  to  lift  the  upper  plate  a  few  centimeters,  and  bring 
it  down  forcibly  upon  the  lower.  If  we  do  so,  keeping 
the  surfaces  parallel,  we  shall  be  made  aware  by  the  dull 
sound  uttered  at  impact,  —  altogether  different  from  the 
semi-metallic  ring  of  glass  against  glass,  —  also  by  the 
yielding  character  of  the  material  against  which  the  upper 
plate  impinges,  that  we  do  not  bring  the  two  glass  surfaces 
into  contact  at  all. 

It  is  an  air  cushion  which  receives  the  blow,  and  the 
effect,  both  as  to  the  sound  and  the  character  of  the 


COHESION,   ADHESION,   AND  FRICTION 


87 


impact,  is  very  like  that  which  would  be  obtained  were 
a  thin  film  of  soft  rubber  interposed. 

This  film  of  air  can  be  in  great  measure  removed  by 
pressing  the  plates  together,  and  by  sliding  them  back 
and  forth  upon  one  another.  Then,  if  the  surfaces  be 
clean,  so  that  no  grains  of  dirt  keep  them  apart,  and,  if 
the  surfaces  be  parallel  (which  is  by  no  means  always  the 
case  with  chance  specimens  of  glass),  they  will  come  well 
into  the  range  of  the  action  of  the  molecular  forces,  and 
the  lower  plate,  if  the  upper  one  be  lifted,  will  cling  to  it 
permanently. 

That  this  phenomenon  is  indeed  chiefly  due  to  the 
molecular  forces,  and  not  to  atmospheric  pressure,  may 
be  shown  by  means  of  the  following  experiment : 

79.    EXPERIMENT  15.  —  Adhesion  of  Glass  Plates  in  Vacuo. 

Apparatus : 

(1)  Two  glass  plates  with  plane  faces. 

(2)  An  air  pump. 

Procedure : 

(a)  The  plates  are  thoroughly  cleaned  and 
one  is  laid  upon  the  other.  If  the  surfaces 
match  well  enough  to  enable  one  to  lift  the 
lower  by  its  adhesion  to  the  upper  they  will  serve ; 
if  not,  other  plates  must  be  tried. 

(6)  If  a  bell  jar  of  the  form  shown  in  Fig.  67 
is  available,  it  should  be  selected  for  this  experi- 
ment. In  this  receiver,  which  is  a  well-known 
form,  a  brass  rod  passes  through  the  metal  cap 
(fc)  with  freedom  of  vertical  motion. 

To  the  upper  face  of  the  upper  glass  plate  glue 
a  disk  of  bristol-board,  and  to  the  center  of  this 
fasten  the  end   of  the  brass  rod  by  means   of 
sealing-wax  or   other  cement,  in   such  position  that  the  plate  will 
be  horizontal  when  the  bell  jar  is  in  place. 

(c)  Bring  the  lower  glass  plate  into  its  place,  working  it  as  well 


FIG.  67. 


88 


THE   OUTLINES   OF  PHYSICS 


into  close  contact  with  the  upper  as  is  possible  without  endangering 
the  fastening  of  the  latter.  Invert  the  bell  jar  over  the  plate  of  the 
air  pump,  giving  the  glass  plates  support  until  they  are  in  a  hori- 
zontal position.  Then  the  bell  jar  being  in  place,  lower  the  plates 
by  means  of  the  rod  until  they  rest  upon  a  block  previously  adjusted 
to  receive  them.  After  exhausting  the  air,  the  rod  may  be  raised 
again,  carrying  both  plates  with  it.  It  will  be  found  that  their  attrac- 
tion for  one  another  is  decidedly  greater  after  the  exhaustion,  on 
account  of  the  absence  of  the  air  film  which  had  previously  inter- 
vened. 

80.    EXPERIMENT  16.  —  Cohesive  Forces  in  the  Case  of  Water. 
Apparatus : 

(1)  A  simple  balance  and  a  set  of  weights. 

(2)  A  glass  disk  about  10  cm.  in  diameter;  a  battery  jar  or  other 
glass  dish  of  somewhat  greater  diameter  than  the  disk. 

Procedure  : 

(a)  Remove  one  of  the  scale  pans  from  the  balance  and  hang  in  its 
place  the  glass  disk,  its  surface  carefully  leveled  (Fig.  68).     The  height 


FIG.  68. 

of  the  lower  surface  of  the  disk  should  be  such  that  when  the  balance 
arm  is  level  it  will  be  1  or  2  cm.  above  the  rim  of  the  jar.  Balance 
the  disk  and  place  directly  under  it  the  jar,  which  is  then  to  be  filled 
to  the  brim  with  water. 

(&)  Cause  the  disk  to  fall  gently  upon  the  surface  of  the  water  by 
removing  a  weight  from  the  scale  pan,  and  take  pains  that  no  con- 
siderable air-bubbles  are  entrapped  beneath  the  glass.  Now  add 


COHESION,  ADHESION,  AND  FRICTION  89 

weights   gradually  to   the   scale  pan   and   note    the   following  phe- 
nomena : 

(1)  A  very  considerable  excess  of  weight  over  that  necessary  to  bal- 
ance the  disk  in  air  can  be  placed  upon  the  scale  pan  at  the  other  end 
of  the  balance  beam  without  tearing  the  disk  loose  from  the  water 
upon  which  it  rests. 

(2)  As  weights  are  added,  the  disk  rises  above  the  general  level  of 
the  liquid,  lifting  the  underlying  portions  with  it.     The  surface  of  the 
water  becomes  curved,  as  shown  in  the  figure,  rising  on  every  side  to 
meet  the  periphery  of  the  disk. 

(3)  When  the  disk  finally  leaves  the  water  it  comes  away  with  wetted 
surface. 

This  indicates  that  of  the  two  sets  of  molecular  forces  brought  into 
play  by  the  experiment,  the  attraction  of  the  glass  for  the  contiguous 
water  particles  was  greater  than  that  of  those  particles  for  the  liquid 
next  to  which  they  were  situated.  This  is  the  case  whenever  a  solid 
dipped  into  a  liquid  has  its  surface  wetted  by  the  same. 

If  mercury  be  substituted  for  water  in  this  experiment,  the  same 
phenomena  are  observed,  excepting  that  the  plate,  after  a  considerably 
greater  force  has  been  applied,  is  detached  with  its  surface  dry.  We 
conclude  from  this  form  of  the  experiment  that  the  attraction  between 
glass  and  mercury  is  less  than  between  mercury  and  mercury,  and,  a  forti- 
ori, that  the  latter  is  much  greater  than  the  cohesive  force  of  water. 

By  means  of  the  weights  necessary  to  detach  the  disk,  in  the  case 
of  various  liquids,  these  adhesive  and.  cohesive  forces  may  be  com- 
pared and  measured.  The  difficulties  of  controlling  the  conditions 
are  so  great,  however,  that  the  determination  is  one  not  to  be  recom- 
mended to  the  beginner. 

81.  Friction. — The  resistance  which  the  molecular  forces 
offer  to  the  motion  of  a  body  that  slides  along  a  surface 
with  which  it  is  in  contact,  is  termed  sliding  friction. 

It  is  measured  by  means  of  the  force  necessary  to  main- 
tain the  sliding  body  in  uniform  motion  along  a  horizontal 
surface  of  the  character  in  question. 

82.  Coefficient  of  Sliding  Friction.  —  The    coefficient   of 
sliding  friction  is  the  ratio  of  the  force  necessary  to  main- 


90 


THE  OUTLINES   OF  PHYSICS 


tain  a  sliding  body  in  uniform  motion  to  the  force  with 
which  the  latter  presses  against  the  surface  upon  which 
it  slides.  Thus  in  Fig.  69,  50  kg.  are  kept  in  uniform 


50  K 


AL 


m  i  g  -  (50,000  x  980)  dynes 


h— HioK 

f  -  (10,000  x  980)  dynes 


FIG.  69. 

motion  along  the  horizontal  plane  AB  by  the  force  due 
to  the  attraction  of  the  earth  upon  10  kg.  The  forces  in 
question  are 

50,000  x  980  dynes 

and  20,000  x  980  dynes. 

The  ratio  of  the  two  is 

:  1  =  -20, 
5 

which  is  the  coefficient  of  sliding  friction. 

83.   EXPERIMENT  17.  —  Laws  of  Sliding  Friction. 

Apparatus : 

(1)  An  inclined  plane  of  soft  wood,  about  100  cm.  long.     At  one 
end  this  plane  is  hinged  to  a  substantial  base.     The  other  end  plays 
between  two  stiff  uprights  to  which  it  can  readily  be  clamped  at  any 
desired  angle.     The  upper  surface  of  the  plane  is  to  be  freshly  sand- 
papered before  the  beginning  of  the  measurements. 

(2)  A  wooden  block  20  cm.  x  10  cm.  x  5  cm.,  also  freshly  sand- 
papered.    In  the  middle  of  one  of  the  broader  sides  is  bored  a  hole, 


COHESION,   ADHESION,   AND  FRICTION 


91 


into  which  fits  a  tall  wooden  peg.     The  same  peg  may  also  be  used 
in  a  similar  hole  in  the  middle  of  one  of  the  narrower  sides. 

(3)  Several  5  kg.  iron  disk  weights,  a  meter  scale,  some  joiner's 
clamps,  and  a  wedge. 

Procedure : 

(a)  The  inclined  plane  is  clamped  to  a  table,  as  in  Fig.  70.  The 
wooden  block  is  placed  upon  the  plane  and  the  free  end  is  lifted  until 
the  block,  when  tapped  into  motion  with  the  finger,  shows  a  tendency 
to  continue  sliding. 


U" 


FIG.  70. 

(&)  Fasten  two  joiner's  clamps  to  the  uprights  just  below  the  plane, 
to  afford  a  support  for  the  latter,  insert  the  wedge  (w),  which  must  be 
broad  enough  to  reach  across  between  the  clamps. 

By  means  of  the  wedge  adjust  the  pitch  further,  until  the  critical 
angle  is  found,  i.e.  the  angle  at  which  the  block,  once  started,  will  con- 
tinue to  slide  with  a  uniform  motion. 

That  this  angle  measures  the  coefficient  of  friction  is  evident  from 
a  consideration  of  forces  acting  upon  the  sliding  body.  The  force 
mg  between  the  earth  and  a  body  on  an  inclined  plane  (as  in  some 


92  THE  OUTLINES   OF  PHYSICS 

previous  examples)  is  resolved  into  p  and  /  (Fig.  71),  the  functions 
of  which  are  to  produce  pressure  against  the  plane  and  motion  along 

the  same  respectively.  The  ratio  -  is  therefore  the  coefficient  of 
friction.  Since  the  triangle  of  forces  in  this  case,  however,  is  similar 
to  ABC,  the  triangle  made  by  the  plane,  its  base,  and  its  upright,  the 

JO/"* 

ratio  likewise  measures  the  coefficient. 

AC 

(c)  By  means  of  the  present  experi- 
ment the  following  laws  of  friction  are 
to  be  verified  : 

(1)  The  friction  is  proportional  to  the 
pressure;  i.e.  to  the  mass  moved.  Other- 
wise stated,  this  means  that  the  coeffi- 
dent  is  a  constant  and  is  independent 
of  the  mass  employed. 

(2)   The  friction  is  independent  of  the  area  of  surfaces  in  contact. 
To  demonstrate  the  first  law,  insert  the  peg  in  the  block,  and  load 
the  latter  successively  with  5  kg.,  10  kg.,  15  kg.,  and  20  kg.     It  will 
be  found  that  the  critical  angle  is  the  same  for  all  loads. 

To  demonstrate  the  second  law,  turn  the  block  upon  its  edge  and 
repeat  the  determination.  It  will  be  found  that  the  critical  angle 
is  still  unchanged. 

(c?)  Determine  the  coefficient  for  the  following  substances. 

(1)  A  piece  of  plate  glass  sliding  upon  wood. 

(2)  A  piece  of  plate  glass  sliding  upon  glass. 

(3)  A  piece  of  polished  metal  (not  lacquered)  sliding  upon  wood. 

(4)  Paper  upon  wood.     (For  this  purpose,  paste  smoothly  a  piece 
of  paper  to  one  face  of  a  wooden  block ;    sand  paper  the  edges  and 
test  it  upon  the  wooden  plane.) 


84.  Starting  Friction.  —  This  term  is  used  for  the  force 
necessary  to  start  a  body  into  motion  upon  a  horizontal  sur- 
face. The  apparatus  just  described  will  serve  for  the 
demonstration  of  the  following  points,  with  reference  to 
starting  friction : 

(1)  Starting  friction  always  exceeds  sliding  friction. 
(It  will  be  found  that,  when  the  plane  is  at  the  critical 


COHESION,   ADHESION,   AND  FRICTION 


93 


angle,  the  block  may  be  placed  upon  it  and  will  remain 
at  rest.) 

(2)  To  start  the  block  the  angle  must  be  considerably 
increased.  The  increase  is  not  constant,  however.  Start- 
ing friction  is  variable,  and  depends  upon  the  extent  to 
which  the  molecular  forces  are  brought  to  bear  upon  the 
resting  mass.  Once  started,  the  sliding  body  comes  into 
a  constant  relation  to  these  forces. 

The  following  experiment  upon  starting  friction  is 
instructive : 

85.    EXPERIMENT   18.  —  Starting  Friction  of  a  Lubricated  Surface. 

Apparatus : 

The  inclined  plane  described  in  Experiment  17 ;  also  two  glass 
plates.  (One  longer  than  the  other.) 

Procedure  : 

(a)  Secure  the  longer  plate  to  the  plane  by  means  of  rubber  bands 
or  twine. 


FIG.  72. 

(&)  Flood  the  upper  surface  of  the  plate  with  water  and  lay  the 
other  lightly  upon  it.  It  will  be  found  that  the  critical  angle  is  ex- 
ceedingly small.  Indeed,  it  is  difficult  to  level  the  apparatus  accu- 
rately enough  to  prevent  the  upper  plate  from  sliding. 

(c)  Press  the  plates  together  for  an  instant,  thus  reducing  the 
intervening  layer  of  water  to  a  thin  fiber.  The  plane  may  now  be 
raised  to  90°,  as  in  Fig.  72,  without  causing  the  upper  plate  to  slip. 

(  The  coefficient  of  starting  friction  has  risen  from  an  infinitesimal  value 
to  more  than  unity.") 

If  the  experiment  be  repeated  with  oil  the  result  will  be  the  same. 


94  THE  OUTLINES   OF  PHYSICS 

86.  Rolling  Friction,  —  The  term  friction  has  been  ap- 
plied, although  inaptly,  also   to   the   resistance   which  a 
rolling  body  experiences.     The  French  physicist,  Coulomb, 
who  investigated  the  subject  with  great  care,  found  the 
resistance  to  rolling  to  be  directly  proportional  to  the  pres- 
sure and  inversely  proportional  to  the  radius  of  the  ivheel. 

87.  Friction  of  a  Shaft  in  its  Bearings.  —  This  is  an  inter- 
esting and  important  case  of  sliding  friction.     It  may  be 
briefly  stated  that  the  shaft  rolls  in  its  bearing  until  the 
line  of  contact  is  upon  a  portion  of  the  surface  of  the  latter, 


FIG.  73. 


c  (Fig.  73),  the  tangent  to  which  makes  the  critical  angle 
with  the  horizon.  Then  it  begins  to  slide.  The  materials 
of  the  shaft  and  bearing  are  selected  with  a  view  to  the 
reduction  of  the  angle  a  to  a  minimum,  and  lubricants 
are  applied  for  the  same  purpose. 


ELASTICITY  95 


CHAPTER   XI 
ELASTICITY 

88.  Stress  and  Strain.  —  All  material  bodies  owe  their 
structure,  volume,  and  form  to  the  interaction  of  the  molec- 
ular forces  between  the  particles  of  which  they  are  com- 
posed. These  forces  are  in  equilibrium.  When  forces 
from  without  are  brought  to  bear,  this  equilibrium  is  dis- 
turbed, and  there  are  movements  of  all  the  particles  with 
reference  to  each  other.  These  movements  continue  until 
equilibrium  is  re-established.  The  body  is  then  said  to  be 
under  stress,  and  the  distortion  which  results  is  called 
strain. 

The  changes  which  are  thus  brought  about  are  of  two 
kinds,  viz. : 

(1)  Changes  of  form. 

(2)  Changes  of  volume. 

When  the  body  is  again  released  from  the  action  of  the 
outer  forces,  it  tends  to  return  to  its  former  volume  and 
shape. 

A  body  which  returns  completely  to  its  former  shape  is 
said  to  have  perfect  elasticity  of  form ;  a  body  which  re- 
sumes exactly  its  former  volume  has  perfect  elasticity  of 
volume. 

The  term  elasticity  is  also  used  with  reference  to  the 
power  of  resisting  change  of  form  or  volume. 

Fluids,  on  account  of  the  greater  freedom  or  mobility  of 
their  molecules,  do  not  ordinarily  possess  elasticity  of  form, 
but  their  elasticity  of  volume  is  perfect. 


96 


THE   OUTLINES   OF  PHYSICS 


89.  Limit  of  Elasticity. —  Solids  possess  elasticity  both 
of  form  and  volume.  When  the  stress  passes  a  certain 
value,  however,  the  solid  no  longer  returns  to  its  original 
condition;  it  is  then  permanently  distorted.  We  say  in 
such  a  case  that  the  limit  of  elasticity  has  been  passed. 

It  will  be  possible  to  consider  in  this  book  only  a  few  of 
the  simplest  phenomena  in  the  domain  of  elasticity.1 


90.   EXPERIMENT 
of  a  Wire. 


19.  —  Relation  of  Stretching  Force  to  Elongation 


q  1. 1    '  ;  i> 


It  is  the  object  of  this  experiment  to  study  the 
behavior  of  a  wire  which  is  subjected  to  homo- 
geneous longitudinal  stress. 

Apparatus: 

(1)  A  fine  wire   of  brass   or  steel,  suspended 
vertically.      (Pianoforte   wire,    about  -04   cm.    in 
diameter  is  to  be  preferred.) 

(2)  A  set  of  iron  disk  weights  with  hook;    a 
meter  scale. 

(3)  A  pair  of  microscopes  of  low  power,  pro- 
vided with  eyepiece  micrometers.     (See  Appen- 
dix IY.)     (If  due  care  be  taken  with  reference  to 
the  rigidness  of  support  of  the  wire,  one  of  these 
may  be  dispensed  with  without  seriously  vitiating 
the  result.) 

One  of  the  simplest  forms  which  the  apparatus 
for  this  experiment  may  be  given  is  that  shown  in 
Fig.  74. 

It  consists  essentially  of  a  pair  of  substantial 
wall-brackets,  placed  about  150  cm.  apart,  with  two 
connecting  vertical  wooden  strips.  One  of  these 
is  fastened  to  the  wall  of  the  laboratory,  while 
the  other,  AB,  supports  the  microscopes. 

The  wire  is  fastened  above  in  a  clamp  with 
steel  jaws.  (An  ordinary  hand-vise  makes  an  ex- 
cellent clamp  for  this  purpose.)  It  then  passes 

1  For  an  elementary  discussion  of  the  theory,  see  Elements  of  Physics, 
p.  83. 


FIG.  74. 


ELASTICITY  97 

through  a  hole  in  the  upper  bracket.  The  lower  end  is  attached 
to  the  hook  of  a  1  kg.  weight  as  shown  in  the  figure.  The  weight, 
the  hook  of  which  passes  through  a  hole  in  the  lower  bracket,  keeps 
the  wire  tense. 

To  mark  upon  the  wire  two  points,  the  movements  of  which  are  to 
be  observed,  take  a  hair,  and  loop  it  around  the  wire  opposite  each 
microscope.  Draw  it  taut,  using  a  single 
knot,  then  shift  it  along  the  wire  gentlv 
with  a  match  end  or  splinter  of  wood, 
until  it  is  within  the  field  of  the  microscope 
and  near  the  (apparently)  lower  end  of  the 
scale.  Dip  the  splinter  into  a  shellac  solu- 
tion and  touch  the  knot,  which  should  be 
on  the  side  of  the  wire  away  from  the 
microscope.  As  seen  in  the  field  of  the 
microscope,  the  wire  and  marker  will  pre- 
sent the  appearance  shown  in  Fig.  75.  FlG- 

To  prevent  troublesome  oscillation  and  the  turning  of  the  wire,  the 
following  device  may  be  employed.  It  consists  of  a  pulley  fastened 
to  a  wooden  block.  Upon  this  block  is 
placed  another  smaller  one.  Around 
the  wire,  about  10  cm.  above  the  lower 
bracket,  is  twisted  a  smaller  wire,  the 
free  ends  of  which  project  horizon-  [ 

tally.  One  of  these,  coming  into  con- 
tact with  the  smaller  block,  prevents 
the  stretched  wire  from  turning.  The 

pulley,  which  is  pushed  forward  until  . 

its  face  is  in  light  contact  with  the 

latter,   checks  its  oscillations.      This 

little  device  is  not  fastened  to  the  bracket,  but  is  adjusted  as  may 

be  necessary,  with  the  hand. 

The  microscopes  are  inserted  through  holes,  about  1  m.  apart, 
which  are  bored  in  the  upright  piece,  AB.  They  should  fit  the  holes 
snugly,  but  should  be  adjustable  for  the  purpose  of  rough  focussing. 

Procedure : 

(CL)  Place  the  suspended  wire  under  the  tension  of  a  kilogram 
weight. 

(&)  Focus  the  microscopes  (a)  and  (6)  upon  their  respective  markers, 


98 


THE  OUTLINES   OF  PHYSICS 


and  note  the  positions  of  the  latter  by  means  of  the  micrometer 
scales. 

(c)  Add  carefully  four  kilogram  weights,  and  observe  the  positions 
of  the  markers  after  the  addition. 

(rf)  Remove  the  weights  stepwise,  redetermining  the  position  of 
the  markers  after  each  change;  then  restore  the  weights,  one  at  a 
time,  continuing  to  read  the  positions,  until  the  full  load  has  been 
restored. 

The  results  of  these  observations  should  afford  a  verification  of  the 
law  that  the  elongation  is  proportional  to  the  stretching  force. 

(e)  Tabulate  the  results  obtained,  as  follows,  and  from  them  plot 
a  curve  for  increasing  and  decreasing  weights. 

TABLE. 
OBSERVATIONS  UPON  THE  STRETCHING  OF  A  WIRE. 


Position  of  the  marks. 

„,      ,   ,  .              .   ,  ,        J 

Lower. 

Upper. 

4000  g. 

34-7 

21-6 

3000  g. 

26-4 

20-4 

2000  g. 

18-9 

19-6 

1000  g. 

10-4 

18-6 

0 

1-8 

17-2 

1000  g. 

10-2 

18-9 

2000  g. 

18-7 

19-8 

3000  g. 

26-3 

20-7 

4000  g. 

34-6 

21-5 

From  these  readings  we  can  easily  compute  the  movement  of  the 
upper  and  lower  marks,  by  subtracting  each  from  1-8  for  the  latter 
and  from  17-2  for  the  former.  The  movement  of  the  lower  mark 


1  The  weight  previously  applied,  i.e.  I  kg.,  to  keep  the  wire  taut  is  not 
included,  nor  need  it  be  since  the  object  of  the  measurements  is  to  deter- 
mine  the  influence  of  changes  in  the  stretching  weight. 


ELASTICITY 


99 


minus  that  of  the  upper  gives  the  total  elongation,  and  this  divided 
by  the  corresponding  stretching  weight  (m)  gives  the  elongation  per 
gram. 


M. 

Movement  of  the  marks. 

Total  elongation 
(A£)  expressed 
in  scale  divi- 
sions. 

Elongation  per 
gram  of  stretching 
weight. 

Lower. 

Upper. 

4000  g. 

32-9 

4-4 

28-5 

0-07125 

3000  g. 

24-6 

3-2 

21-4 

0-07133 

2000  g. 

17-1 

2-4 

14-7 

0-07175 

1000  g. 

8-6 

1-4 

7-2 

0-07200 

0 

0 

0 

0 

0 

1000  g. 

8-4 

1-7 

6-7 

0-06700 

2000  g. 

16-9 

2-6 

14-3 

0-07150 

3000  g. 

24-5 

3-5 

21-0 

0-70000 

4000  g. 

32-8 

4-3 

28-5 

0-71250 

20000  g. 

142-3 

The  average  elongation  per  gram  is  obtained  by  dividing  the  sum 
of  the  total  elongations  by  the  sum  of  the  stretching  weights.  This 
gives  us 

142-3  s.  d.  -  20000  =  0-07115  s.  d.  per  gram. 

For  the  method  by  which  scale  divisions  may  be  reduced  to  centi- 
meters, and  the  stretch  modulus  of  the  wire  obtained  from  these 
readings,  see  Experiment  20. 

The  data  in  the  foregoing  table  are  intended  to  indicate  the 
character  of  the  results  which  may  be  obtained  with  the  apparatus 
just  described.  They  are  given  graphically  in  Fig.  77,  for  the  pur- 
pose of  showing  the  method  of  treating  such  data.  Ordinates  are 
total  elongations  (AZ)  expressed  in  scale  divisions,  and  abscissas  are 
weights  in  grams  (multiplied  by  g  =  980  they  become  dynes). 

The  fact  that  the  observations  lie  along  a  straight  line  verifies  the 
above-mentioned  relation,  i.e.  proportionality  of  stretching  force  and 
elongation.  Their  close  coincidence  with  one  another  pair-wise  indi- 
cates that  within  the  range  of  this  experiment  steel  is  very  nearly 
perfectly  elastic. 


100 


THE  OUTLINES   OF  PHYSICS 


re. 


;  i  ,  )-L 


<    »-- 


10 


30 


FIG.  77. 


91.  EXPERIMENT  20.  —  The  Stretch  Modulus  (sometimes  called 
Young's  Modulus)  of  a  Steel  Wire.  —  Were  observations  like  those 
of  the  foregoing  experiment  extended  to  wires  of  various  diameters, 
it  would  be  found  that  the  elongation  for  a  given  force  is  inversely 
proportional  to  the  cross-section  (q)  of  the  wire. 


ELASTICITY  101 

Assuming  this  relation,  which  indeed  is  too  evident  to  require 
verification,  we  may  use  the  data  obtained  in  that  experiment  for  the 
quantitative  determination  of  the  modulus  of  the  wire. 

This  quantity,  which,  to  distinguish  it  from  other  coefficients  in 
use  in  the  study  of  elasticity,  is  called  the  stretch  modulus,  or  some- 
times Young's  modulus,  is  a  constant  by  means  of  which  the  power  of 
a  substance  such  as  steel  to  resist  elongation  is  quantitatively  ex- 
pressed.    If  we  call  the  elongation  A/,  we  shall  have : 
A/  :  .F,  where  F  is  the  stretching  force. 
A/  :  I,    where  I  is  the  length  of  the  wire. 

AZ  :  -,   where  q  is  the  cross-section. 

These  relations  may  be  embodied  in  an  equation, 

1  Fl 

AZ  =  =  — , 
E   q 

where  —  is  a  constant  depending  upon  the  nature  of  the  material  of 

±ij 

which  the  wire  is  made.     The  quantity  E  is  called  the  stretch  modu- 
lus ;  its  value  is  evidently 

F       Fl 

-^A7 

It  expresses  numerically  the  resistance  to  stretching,  and  conse- 
quently is  chosen  in  such  a  way  as  to  be  inversely  proportional  to  the 
elongation.  ,  . 

To  find  the  value  of  E  in.  the  case  of  the  wire  under  observation 
we  must  know : 

(1)  The  force  in  dynes.     This  will  be  F  =  m  •  g  dynes. 

(2)  The   length   I,  in   centimeters,  between   the   markers.     This 
measurement  need  not  be  more  exact  than  that  of  the  small  quan- 
tities q  and  AL     The  apparently  rough  method  of  measuring  from 
the  middle  of  the  eyepiece  of  (a)  to  the  middle  of  the  eyepiece  of 
(ft),  with  an  ordinary  meter  scale,  is  abundantly  accurate. 

(3)  The  cross-section  (17).     This  may  be  measured  by  means  of  a 
micrometer  gauge,  or  a  piece  of  the  same  wire  100  cm.  in  length  may  be 
weighed,  and  its  cross-section  computed  upon  the  assumption  that  the 

densitv  is  7-85  (for  steel).     (We  have  for  this  computation  q  =  -^-. 

a  •  I 

where  m  is  the  mass  of  the  weighed  piece,  I  its  length,  and  d  its 
density.) 


102  THE  OUTLINES   OF  PHYSICS 

(4)  The  elongation,  A/,  in  centimeters. 

For  this  purpose  the  eyepiece  micrometers  must  be  calibrated. 
(Without  changing  the  distance  between  eyepiece  and  objective,  turn 
the  eyepieces  so  that  the  micrometer  scale  in  each  has  its  lines  parallel 
to  the  wire,  and  note  to  tenths  of  a  scale  division  the  space  which 
the  wire  occupies  upon  the  micrometer  scale.  From  this,  and  value 
of  the  diameter,  compute  the  value  of  one  scale  division  in  centimeters.) 

From  the  curve  of  elongations  read  the  ordinate  corresponding  to 
a  given  force  (mg)>  This  value  is  in  scale  divisions  of  the  microm- 
eter: reduce  it  to  centimeters. 

Having  thus  found  I,  A/,  and  #,  in  centimeters,  and  ing  =  F  in 
dynes,  E  is  determined.  It  is  a  very  large  number  indeed,  being, 
in  fact,  the  force  in  dynes  necessary  to  stretch  a  rod  of  steel  1  cm.  in 
cross-section  to  double  its  length  (were  that  possible  without  passing 
the  limit  of  elasticity). 

The  following  is  the  computation,  for  example,  of  the  modulus  of 
the  steel  wire,  data  for  the  stretching  of  which  were  given  in  Experi- 
ment 19  (Art.  90). 

Length  of  wire  between  marks     =  /  =  100  cm. 

Sum  of  stretching  forces  applied  =  20,000  g. 

=  980  x  20,000  dynes 
=  19,600,000  dynes  =  F. 

Diameter  as  measured  with  micrometer  gauge  =  -039  cm. 

radius  =  r  =  %  diam.  =  -0195  cm. 

cross-section  =  q  —  ?rr2  =  -00119  cm".2 

Sum  of  elongations  expressed  in  scale  divisions  =  142-3  s.  d. 

Diameter  of  the  wire  in  scale  divisions  7-9  s.  d. 

Value  of  1  s.  d.  in  centimeters  =  — — -  =  -0049  +  cm. 

i  *y 

Sum  of  elongations  in  centimeters  =  142-3  x  -0049  =  -697  cm. 
Substituting  these  values  in  the  formula, 
F.I. 

=  £AT 

we  haye   19>600>Q°0  x  100  =  2,360,000,000,000  =  2-36  x  10" 
"Uuiiy  x  *o97 

=  stretch  modulus  for  steel. 

92.  Other  Phenomena  resulting  from  Longitudinal  Stress.  — 
That  the  diameter  of  a  tube  diminishes  when  the  tube  is 


ELASTICITY 


103 


under  longitudinal  stress  can  be  easily  shown  by  stretching 
an  ordinary  rubber  tube  between  the  hands.  What  is  true 
of  caoutchouc  can  be  shown  by  refined  methods  to  be  true 
even  in  such  rigid  materials  as  glass  and  steel,  and  what 
is  true  of  a  tube  will  be  found  true  in  the  case  of  rods  and 


wires. 


FIG.  78. 


FIG.  79. 


If  we  could  select  a  small  spherical  element  or  portion 
in  the  interior  of  a  rod,  and  observe  its  change  of  form 
when  the  rod  is  stretched,  we  should  find  the  sphere  con- 
verted into  an  ellipsoid  with  the  major  axis  in  the  direction 
of  the  pull  (Fig.  78). 

What  happens  to  this  particular  particle  is,  however,  hap- 
pening to  all  its  neighbors,  and  we  may  extend  our  consid- 


104 


THE  OUTLINES  OF  PHYSICS 


eration  to  a  large  sphere.  Suppose  the  sphere  to  have  a 
diameter  equal  to  that  of  the  rod.  When  the  rod  is  stretched 
its  surface  will  be  tangent  to  the  ellipsoid  into  which  the 
strained  sphere  has  been  converted.  (See  Fig.  79.) 

In  spite  of  this  diminution  of  diameter  the  volume  of 
the  rod  or  tube  is  increased  by  stretching,  as  may  be  shown 
by  means  of  the  following  simple  experiment : 

93.  EXPERIMENT  21.  —  Influence  of  stretching  upon  the  Volume  of 
a  Tube. 

Apparatus  : 

A  rubber  tube ;  a  piece  of  barometer  tubing 
which  fits  the  bore  of  the  former ;  disk  weights 
with  hook. 

About  10  cm.  of  the  barometer  tubing  (any 
thick-walled  glass  tube  will  do)  is  cut  off,  and 
one  end  is  closed  in  the  flame  of  a  blast-lamp 
and  blown  into  a  small  strong  bulb  (Fig.  80). 

In  the  middle  of  a  leather  strap,  30  cm. 
long,  a  hole  is  cut  of  such  size  as  to  allow  the 
tube  to  be  passed  through,  but  not  large  enough 
to  admit  the  bulb.  The  free  ends  are  fastened 
so  as  to  form  a  strong  loop. 

The  closed  glass  tube  is  now  inserted  into  one 
end  of  the  rubber  tube  and  the  remaining  piece 
of  glass  tubing  into  the  other,  and  both  are 
securely  wired  (Fig.  81). 

Procedure : 

(a)  Clamp  the  rubber  tube  in  a  vertical  posi- 
tion to  a  substantial  support,  as  shown  in  Fig. 
81,  and  fill  it  with  water  until  the  surface  of  the 
liquid  is  in  the  upper  part  of  the  open  glass  tube 
at  w. 

(b)  Hang  weights  (5  to  10  kg.)  to  the  strap, 
and  note  the  marked  fall  in  the  level  of  the  col- 
umn of  water. 

The  same  effect  can  be  demonstrated  in  the  case  of  glass  by  means 
of  the  apparatus  depicted  in  Fig.  82. 


FIG.  81. 


FIG.  80. 


ELASTICITY  105 

This  consists  simply  of  a  strong  glass  tube,  closed  at  one  end  and 
enlarged  sufficiently  to  facilitate  the  application  of  weights  by  the 
method  just  described.  The  tube  is  nearly  filled  with  water,  and  the 
end  is  then  drawn  out  into  a  capillary  neck  and  bent  twice  through 
90° ;  after  which  the  filling  is  completed  by  successive  heatings  and 
coolings  of  the  tube. 

-J 

FIG.  82. 

The  effect  in  glass  is  exceedingly  small  on  account  of  the  high- 
stretch  modulus  of  this  substance.  It  is  easily  observable,  however, 
if  the  bore  of  the  neck  is  very  narrow.  The  apparatus  is  a  sensitive 
thermometer,  and  on  that  and  other  accounts  the  experiment  is  a  more 
difficult  one  than  the  foregoing. 

94.  Elasticity  of  Torsion. — When  outer  forces  producing 
stress  are  so  applied  as  to  twist  a  body  about  a  given 
axis,  the  tendency  of  the  body  to  resist  such  twisting,  and 
when  released,  to  return  to  its  original  position,  is  termed 
elasticity  of  torsion. 

The  relation  between  the  force  applied  to  produce  torsion 
and  its  effects,  in  the  case  of  a  rod  one  end  of  which  is 
fixed,  may  be  stated  as  follows : 

Let  0  be  the  angle  through  which  the  free  end  of  the 
rod  is  turned :  then 

0  :  F,  where  F  is  the  torsional  force ; 

0 :  /,  where  I  is  the  length  of  the  twisted  rod ; 

6  :  — ,  where  r  is  the  radius  of  the  twisted  rod. 
r4 

In  the  case  of  torsional  forces,  it  is  really  with  the  moment 
of  the  force  (or  the  torque)  that  we  have  to  do. 


106 


THE  OUTLINES   OF  PHYSICS 


It  can  be  shown  l  that  the  laws  of  torsion  are  fully  ex- 
pressed by  means  of  an  equation 


in  which  ^is  the  torque  (or  moment  of  the  twisting  force), 
and  n  is  a  constant  called  the  constant  of  torsion,  which 
depends  upon,  and  indicates  the  power  of  the  material  to 
resist  torsion. 

The  relations  between  T,  0,  and  Z  are  easily  demon- 
strated by  means  of  the  following  experiment  : 

95.  EXPERIMENT  22.  Torsion  of  a  Rod.  —  It  is  the  object  of  this 
experiment  to  verify  the  fact  that  the  angle  through  which  a  rod  or 
wire,  one  end  of  which  is  fixed,  will  be  twisted  by  a  torsional  force 
applied  at  the  free  end  is  proportional  to  the  length  of  the  rod  and  to  the 
moment  of  the  force. 


Apparatus : 

(1)  A  straight  brass  rod  rather  more  than  100  cm.  long  and  about 
0.5  cm.  in  diameter.  This  must  be  rigidly  fastened  to  a  block  at  one 
end;  10  cm.  from  the  other  end  a  wheel  is  mounted.  (See  Fig.  83.) 

1  See  Elements  of  Physics,  p.  102. 


ELASTICITY  107 

(2)  A  pointer  mounted  upon  a  collar  which  fits  the  rod  and  can 
be  set  and  loosened  at  will ;  also  a  divided  semicircle  capable  of  being 
set  up  in   a  vertical  plane  at  right 

angles  to  and  with  its  center  in  the 
axis  of  the  rod  (Fig.  84). 

(3)  A  meter  scale,  a  set  of  1  kg. 
iron  disk  weights  with  hook. 

Procedure : 

(a)    The  rod  is  mounted  upon  a 

,   «      ,    ,.         .     .,   .  FIG.  84. 

table,  one  end  fixed,  the  wheel  just 

beyond  the  edge  of  the  same,  and  a  second  table  or  stand  affording 
support  for  a  wooden  bearing  (6X),  in  which  the  free  end  of  the  rod 
rests.  The  pressure  upon  this  bearing  is  just  sufficient  to  relieve  the 
rod  from  the  weight  of  the  wheel  (Fig.  83) .  A  second  similar  bear- 
ing (62)  should  be  placed  just  behind  the  wheel. 

(6)  By  means  of  a  cord  running  over  the  periphery  of  the  wheel 
and  to  which  the  disk  weights  may  be  attached,  apply  successively 
1  kg.,  2  kg.,  3  kg.,  4  kg.  The  torque  is  rmg  in  each  case,  where  r  is 
the  radius  of  the  wheel,  and  m  the  mass  of  the  weights  applied. 

Note  that  wherever  the  pointer  may  be  attached  to  the  rod,  with 
circular  scale  behind  it,  it  will  be  turned  through  an  angle 

0  :  rmg. 

Note  further,  that  using  a  given  force  and  placing  the  pointer  at 
different  points  upon  the  rod, 

•,*;*, 
where  I  is  the  distance  from  fixed  end  of  the  rod  to  the  pointer. 


108  THE  OUTLINES   OF  PHYSICS 


CHAPTER   XII 
THE  PROPERTIES  OF  LIQUIDS 

96.  Hydrostatic  Pressure.  —  When  a  fluid,  either  a  liquid 
or  a  gas,  previously  at  rest,  is  subjected  to  any  force, 
motions  will  be  set  up ;  and  these  will  continue  until  an 
arrangement  of  the  parts  of  the  fluid  has  been  attained, 
such  that  at  any  given  point  within  the  same  the  forces  at 
work  counterbalance  each  other  and  thus  have  zero  for 
their  resultant.  The  fluid  will  then  be  under  stress  of 
the  only  kind  to  which  it  is  possible  for  it  to  be  subject 
while  at  rest.  This  type  of  stress  is  called  hydrostatic 
pressure.  The  nature  of  it  is  such  that  if  we  select  any 
imaginary  area  whatever  the  pressure  upon  that  area  will 
be  normal  to  the  same.1 

The  fact  of  the  balance  of  forces  within  a  liquid  at  rest 
may  be  verified  by  the  observation  of  the  form  which  small 
globules  of  any  liquid  assume  when  suspended  in  a  liquid 
mass  with  which  they  do  not  tend  to  mix.  Drops  of  oil 
falling  through  water  afford  the  most  familiar  example. 
The  spherical  form  of  such  drops  is  due  to  the  fact  that 
the  forces  acting  upon  their  surfaces  are  everywhere  normal 
to  the  surface  and  equal  to  one  another. 

The  form  of  soap  bubbles  floating  in  still  air  affords  an 
equally  complete  verification  of  the  principles  in  the  case 
of  gases,  while  the  distortions  which  such  bubbles  undergo 

1  For  a  proof  of  this,  which  is  known  as  Pascal's  principle,  see  Ele- 
ments of  Physics,  p.  87. 


THE  PROPERTIES   OF  LIQUIDS 


109 


when  subjected  to  a  draught  indicate  that  the  principle  is 
to  be  applied  only  to  fluids  at  rest. 

97.    EXPERIMENT  23.  —  The  Transmission  of  Pressure  in  Liquids. 

Apparatus : 

A  glass  cylinder  about  30  cm.  in  height  (Fig.  85),  a  glass  tube  or 
series  of  tubes  coupled  together  and  fitted  so  as  to  enter  the  cylinder 


FIG.  85. 

through  a  water-tight  cork  as  shown  in  the  figure.  These  may  ex- 
tend horizontally  to  any  convenient  distance. 

Procedure : 

(a)  The  cylinder  is  filled  to  the  brim  with  water,  and  a  glass  tube 
t,  the  closed  end  of  which  is  blown  out  to  form  a  bulb,  is  immersed 
therein  with  the  mouth  downwards.  This  tube,  the  air  within  which 
is  somewhat  compressed,  acts  as  a  pressure  gauge. 

(i)  The  cork  is  now  inserted  into  the  mouth  of  the  cylinder,  the 
excess  of  liquid  flowing  into  the  long,  horizontal  tube.  The  latter  is 
completely  filled,  and  its  somewhat  enlarged  aperture  is  closed  by 
means  of  a  membrane  of  soft  rubber. 

This  arrangement  of  the  apparatus  completed,  it  will  be  found  that 
the  water  column  within  the  gauge  will  respond  sharply  to  every 


110 


THE  OUTLINES   OF  PHYSICS 


change  of  pressure  produced  at  the  diaphragm.  However  great  the 
distance  of  the  latter  from  the  cylinder  may  be,  it  is  only  necessary  to 
tap  it  with  the  finger  tip  to  throw  the  water  column  into  oscillation. 

The  observer  should  note  the  promptness  with  which  the  indica- 
tion at  the  gauge  follows  the  movement  of  the  diaphragm.  In  point 
of  fact  the  pressure  is  transmitted  by  means  of  wave  motion  in  the 
liquid.  This  motion  is  much  too  rapid  to  admit  of  direct  observation 
with  the  unaided  eye.  Its  velocity  in  water  is  about  1435  meters  per 
second.  (See  further  the  chapters  on  sound.) 

98.  The  property  of  transmitting  pressure,  described  in 
the  foregoing  experiment,  is  made  use  of  in  the  apparatus 
known  as  the  hydraulic  press.  It  consists  essentially  of  a 
strong,  closed  reservoir  containing  water  or  other  liquid. 
Through  the  walls  of  this  reservoir  play  two  pistons. 
One  of  them,  A  (Fig.  86),  is  of  large,  the  other,  #,  is  of 
small  area. 

The  reservoir  is  always  full,  and  the  pressure  upon  its 
walls,  including  the  areas  of  the  two  pistons,  is  everywhere 
the  same,  and  is  normal  to  the  surface.  Since  by  pressure 
we  mean  the  force  per  unit  of  area,  it  follows  that  loads 
placed  upon  the  two  pistons,  as  in  the  diagram,  will  always 
balance  one  another,  provided  their  masses  are  proportional 

to  the  areas  of  the 
pistons.  Moreover, 
if  the  smaller  piston 
be  forced  downwards 
through  its  cylinder, 
the  larger  piston 
will  rise  and  carry 
its  load  with  it.  If 

FlG  8y  the  ratio  of  the  areas 

be  1,000,000  : 1,  for 

example,  the  force  of  gravity  upon  somewhat  more  than 
one  kilogram  will  serve  to  lift  one  million  kilograms 


THE  PROPERTIES   OF  LIQUIDS 


111 


against  the  earth's  attractive  force.  Note  that  the  law 
of  machines  holds  in  this  case.  The  work  done  by  the 
one  kilogram  in  falling  one  centimeter,  for  instance,  would 
be  980,000  ergs.  The  large  piston  with  its  load  of  1,000,000 
kilograms  would  be  lifted  far  enough  to  afford  room  for 
the  water  displaced  by  the  small  one,  i.e.  0-000001  centi- 
meters, and  this  movement  corresponds  likewise  to  980,000 
ergs.  As  in  the  case  of  nearly  all  machines  for  the  move- 
ment of  very  large  masses  by  the  application  of  small 
forces,  there  is  a  considerable  waste  of  energy  in  overcom- 
ing friction. 


FIG.  87. 


In  order  to  make  the  action  of  the  hydraulic  press  con- 
tinuous, the  smaller  piston  is  driven  like  the  plunger  of  a 
pump  and  operates  a  valve  by  means  of  which  water  is 


112  THE  OUTLINES   OF  PHYSICS 

introduced  into  the  reservoir  at  each  stroke.     A  common 
form  of  press  is  shown  in  Fig.  87. 

99.  The   Distribution   of  Pressures   within  a  Liquid   con- 
tained in   an  Open  Vessel.  —  The   stress   to  which   such  a 
fluid  is  subject  is  that  due  to  the  action  of  gravity  upon 
each  particle,  and  to  the  pressure  of  the  superincumbent 
atmosphere.     For  the  purpose   of   the  present  discussion 
the  latter  may  be  disregarded.      The  following  relations 
are  of  importance : 

(1)  The  pressure   within  a   liquid  mass  increases  from 
the  surface  downwards  in  direct  proportion  to  the  depth. 

(2)  The  pressure  at  a  given  depth  below  the  surface  is 
proportional  to  the  density  of  the  liquid. 

(3)  The  pressure  in  a  given  liquid  is  dependent  only 
upon  the  depth.     It  is  independent  of  the  form  of  the  vessel 
and  of  the  amount  of  liquid  which  it  contains. 

Statements  (1)  and  (2)  may  be  verified  as  follows : 

100.  EXPERIMENT  24.  — Relation  between  Pressure  and  Depth  of 
a  Liquid. 

Apparatus: 

(1)  A  tall  cylindrical  glass  jar. 

(2)  A  glass  funnel  and  tubing;   a  burette  tube  with  two  arms; 
blocks,  supports,  etc. ;  a  wooden  scale. 

Procedure : 

(a)  Bend  a  piece  of  glass  tubing  (jj)  about  80  cm.  long  as  shown 
in  Fig.  88.  Attach  one  end  of  it,  with  an  air-tight  joint  of  rubber 
tubing,  to  a  glass  funnel,  the  other  end  similarly  to  one  arm  of  a 
U-shaped  tube  (preferably  a  double  burette  tube  with  stopcock). 
Support  the  whole  at  such  a  height  above  a  laboratory  table  that  the 
cylindrical  jar,  when  standing  upon  the  table,  will  slide  under  the 
mouth  of  the  funnel. 

(6)  Warm  the  lip  of  the  funnel  and  coat  it  with  beeswax-resin 
cement,  and  while  the  latter  is  still  soft  lay  over  the  mouth  of  the 
funnel  a  thin  diaphragm  of  pure  soft  rubber.  The  diaphragm  should 


THE  PROPERTIES   OF  LIQUIDS 


113 


be  tense  enough  to  form  a  plane  septum,  but  should  not  be  tightly 
stretched. 

(c)  Fill  the  jar  with  water,  place  it  under  the  funnel,  and  raise  it 
by  the  insertion  of  blocks  until  the  mouth  of  the  submerged  funnel 
is  near  the  bottom. 


FIG.  88. 

(c?)  The  upward  pressure  against  the  rubber  diaphragm,  being  un- 
balanced, will  distend  the  latter,  rendering  it  concave,  as  seen  from 
below  (Fig.  89),  and  forcing  it  into  the  funnel. 
This  force  is  now  to  be  balanced  by  pouring 
water  into  the  open  arm  of  the  U-tube,  which 
serves  as  a  pressure  gauge,  until  the  diaphragm 
has  resumed  its  original  plane  contour. 

(e)  Measure  the  difference  of  level  A,  k  of 
the  two  columns  in  the  U-shaped  tube,  also  the 
distance  e,f  from  the  surface  of  the  water  in 
the  jar  to  the  plane  of  the  diaphragm.  Remove 
the  blocks  from  beneath  the  jar,  one  at  a  time, 

and  repeat  the  above  measurements  for  the  various  depths  of  sub- 
mergence thus  obtained.     The  data  should  accord  with  statement  (1). 


FIG.  89. 


114 


THE  OUTLINES   OF  PHYSICS 


(y  )  Fill  the  jar  with  oil,  or  with  strong  brine,  and  repeat  the  deter- 
mination for  a  single  depth.  Water  should  still  be  used  in  the  U-tube. 
Note  that  the  height  hk  is  no  longer  equal  to  ef.  Find  the  density 
of  the  liquid  in  the  jar,  using  one  of  the  methods  described  in  Chap. 
XIII.  The  result  should  verify  the  relation  hk:ef  ::d:l,  or 

hk     , 


In  this  formula  d  is  the  density  of  the  liquid  in  the  jar  as  com- 
pared with  the  density  of  water,  which  is  taken  equal  to  unity. 

The  height,  hk,  of  the  liquid  in  the  U-tube  is  a  measure  of  the 
pressure  upon  the  diaphragm,  and  the  relation  expressed  in  the 
equation  therefore  verifies  statement  (2). 

101.    EXPERIMENT  25.  —  Pascal's  Vases. 

The  statement  that  pressure  within  a  given  liquid  depends  upon 
the  depth  alone,  and  is  independent  of  the  form  and  volume  of  the 
containing  vessel,  may  be  verified  by  means  of  the  following  device, 
which  is  a  modification  of  the  classical 
apparatus  known  as  Pascal's  vases  : 
Apparatus  : 
(1)  A  strong  brass  tube,  about  7  cm. 

I  in  diameter  and  10  cm.  long.     This  car- 

ries  a   broad    flange    at   its   middle,   as 
FlG   90  shown  in  Fig.  90.     One   end,  which   is 

threaded,  fits  any  one  of   three    similar 

tubes,  also  of  brass,  which  form  the  lower  ends  of  three  glass  vessels. 
These  vessels  are  given  widely  different  forms,  as  shown  in  Fig.  91. 

(2)  A  rubber  diaphragm,  which  is  to  be  fastened  to  the  bottom  of 
the  flanged  tube. 


_i 


f- 


FIG.  91. 


THE  PROPERTIES   OF  LIQUIDS 


115 


(3)  A  long  pointer,  pivoted  as  shown  in  Fig.  92. 

(4)  A  scale  along  which  the  pointer  plays. 
Procedure  : 

(«)  The  rubber  diaphragm  is  fastened  to  the  unthreaded  end  of 
the  flanged  tube,  which  may  conveniently  be  constructed  with  a 
sliding  collar  for  securing  the  same. 


\ 


FIG.  92. 


(6)  The  tube  is  mounted  with  the  flange  horizontal  and  diaphragm 
below,  as  shown  in  Fig.  92,  and  one  of  the  glass  receptacles  with  its 
brass  base  is  screwed  into  place  above.  We  thus  have  a  vessel  with 
a  flexible  bottom  and  capable  of  being  filled  with  water. 

(c)  The  pointer  is  adjusted  with  its  short  lever  arm  in  contact  with 
the  middle  of  the  diaphragm  and  the  long  arm  indicating  the  zero 
of  the  scale. 

(d  )  Water  is  poured  into  the  vessel.  The  rubber  diaphragm  being- 
distended  downward  moves  the  pointer  along  the  scale.  When  the 


116  THE   OUTLINES   OF  PHYSICS 

surface  of  the  water  reaches  a  level  previously  marked  near  the  lip  of 
the  vessel,  the  scale  reading  is  noted. 

(e)  The  vessel  is  emptied  with  a  siphon,  and  one  of  the  other 
receptacles  is  substituted  for  the  one  just  used.  The  lower  portion 
should  remain  undisturbed.  The  pointer  being  readjusted  to  zero, 
the  filling  with  water  is  repeated,  the  level  being  brought  to  the  same 
height  above  the  diaphragm. 

(/)  The  operation  is  repeated  with  the  remaining  receptacle  in 
place. 

The  object  of  the  experiment  is  to  show  that  the  pressure  upon 
the  flexible  bottom  is  the  same  for  a  given  height  of  liquid,  whichever' 
receptacle  be  used.  This  fact  is  indicated  by  the  uniformity  of  the 
scale  readings. 

• 

102.   The  Principle  of  Archimedes.  —  It  is  obvious  from 
the  preceding  experiments  that  the  pressure    upon   any 
plane  area  within  a  liquid  at  rest  is  that  due  to  the  weight 
of  the  column  of  superincumbent  liquid. 
Consider  the  case  of  a  submerged  solid 
cylinder    (Fig.    93).     The   pressure    is 
everywhere  normal  to  its  surface,  and 
the  lateral  forces,  which  at  each  point 
are   proportional  to   the  depth    of   the 
point  below  the   surface  of  the  liquid, 
FIG.  93.  precisely  counterbalance    one    another. 

Were  this  not  the  case  there  would 
be  lateral  movement  of  the  cylinder,  which  does  not  occur. 
Upon  the  upper  face  of  the  cylinder  the  force  is  down- 
wards and  is  that  due  to  the  weight  of  the  liquid  column 
aaoo.  The  force  acting  upon  the  lower  face  is  upwards, 
and  is  that  due  to  the  weight  of  a  liquid  column  equal  to 
bboo.  The  resultant  of  these  forces  is  a  force  equivalent 
to  that  due  to  the  weight  of  a  mass  of  liquid  of  the  same 
size  as  the  cylinder  and  acting  vertically  upwards.  If  we 
consider  this  force,  which  is  called  the  buoyant  force  of  the 


THE  PROPERTIES   OF  LIQUIDS 


117 


liquid,  in  connection  with  the  attractive  force  of  the  earth 
upon  the  cylinder,  we  see  that  these  being  opposite  in 
direction  the  result  is  a  loss  of  weight.  The  statement 
of  this  fact  is  known  as  the  principle  of  Archimedes.  It 
is  as  follows : 

A  body,  when  submerged  in  any  liquid,  loses  weight  by  an 
amount  equal  to  the  weight  of  the  liquid  which  it  displaces.1 

.  103.  The  principle  of  Archimedes  is  usually  verified  in 
the  case  of  liquids  by  means  of  what  is  known  as  the 
cylinder  and  bucket  apparatus. 


FIG.  94. 

A  small,  cylindrical,  brass  bucket  is  placed  upon  one 
scale  pan  of  a  balance  (Fig.  94),  beneath  which  hangs  a 
cylinder  which  exactly  fits  the  interior  of  the  bucket.  Its 
volume,  therefore,  is  that  of  the  contents  of  the  bucket. 

1  The  discussion  is  readily  extended  to  the  case  of  bodies  of  irregular 
form.  We  may  regard  such  a  body  as  made  up  of  vertical  rods,  or  ele- 
ments of  infinitesimal  cross-section.  For  each  of  these  taken  separately 
the  considerations  given  above  suffice,  and  what  is  true  of  each  of  these 
elements  will  be  true  of  the  whole  body,  whatever  may  be  its  form. 


118 


THE   OUTLINES   OF  PHYSICS 


If  the  balance  be  brought  into  equilibrium  and,  the  arms 
being  still  free,  a  beaker  of  water  be  brought  up  from 
below,  it  will  be  found  impossible  to  submerge  the  cylin- 
der on  account  of  the  buoyant  force  of  the  fluid.  (See 
preceding  article.) 

If,  however,  water  be  poured  into  the  bucket  by  degrees, 
partial  submergence  of  the  cylinder  will  take  place,  and 
equilibrium  will  be  restored  when  the  portion  submerged 
equals  the  portion  of  the  bucket  which  has  been  filled 
(Fig.  95).  When  the  bucket  is  full,  the  upper  surface  of 


FIG.  95. 

the  cylinder  will  be  at  the  level  of  the  water  in  the 
beaker.  If,  up  to  this  point,  the  top  of  the  cylinder  has 
been  kept  dry,  it  will  be  found  possible  to  carry  the  experi- 
ment a  step  further.  It  is  possible  by  taking  advantage 
of  capillarity,  to  add  a  considerable  quantity  of  water 
to  the  bucket,  sinking  the  cylinder  considerably  below 
the  general  surface  of  the  liquid,  before  the  bucket  over- 
flows or  the  \vater  in  the  beaker  encroaches  upon  the  top 
of  the  cylinder.  This  final  stage  is,  likewise,  indicated 
in  the  figure. 


THE  PROPERTIES   OF  LIQUIDS 


119 


104.  The  Beaker  gains  in  Weight  what  the  Submerged 
Cylinder  loses.  —  By  balancing  the  scales  with  the  beaker 
of  water  upon  one  scale  pan  and  the  bucket  upon  the 
other  (Fig.  96),  and  attempting  to  submerge  the  cylinder 


FIG.  96. 

sustained  from  without  in  the  beaker,  the  reaction  corre- 
sponding to  the  buoyant  force  of  the  liquid  may  be  made 
evident  by  apparent  increase  of  weight  of  the  beaker. 
That  this  reaction  is  precisely  equal  and  opposite  to  the 
buoyant  force  (third  law  of  motion)  may  be  shown  by 
filling  the  bucket  with  water,  by  which  means  equilibrium 
is  restored. 

105.    EXPERIMENT  26.  —  The  Influence  of  Partial  and  Total  Sub- 
mergence upon  the  Weight  of  a  Body. 
Apparatus  : 

(1)  A  balance  and  weights.     The  former  should  be  provided  with 
a  mechanical  device  for  the  arrest  of  the  beam. 

(2)  A  cylindrical  glass  vessel  containing  water.     The  depth  must 
exceed  20  cm. 

(3)  A  scale  divided  to  millimeters  and  a  micrometer  gauge. 


120  THE  OUTLINES   OF  PHYSICS 

(4)  A  cylindrical  rod  of  brass  or  copper  about  20  cm.  long,  also  a 
similar  rod  of  wood,  or  other  light  material,  loaded  at  one  end  with  a 
cylindrical  sinker  of  the  same  diameter  and  of  such  mass  that  the 
rod  will  float  in  a  vertical  position  and  more  than  half  submerged. 
To  take  the  place  of  the  latter  a  floating  tube  may  readily  be  con- 
structed out  of  any  tube  of  thin  metal  closed  at  one  end.  One  of 
the  cases  in  which  thermometers  are  packed  will  serve  the  purpose. 
It  may  be  ballasted  by  the  introduction  of  shot,  and  then  capped  at 
the  upper  end. 

Procedure : 

(a)  Measure  the  diameter  of  the  heavier  rod  with  the  gauge,  and 
compute  its  volume  per  centimeter  of  length  in  cubic  centimeters. 

(ft)  Beginning  at  one  end  of  the  rod,  which  end  should  be  plane  and 
normal  to  the  axis  of  the  rod,  graduate  the  latter  in  centimeters,  and 
mark  the  divisions  by  means  of  a  triangular  file  ground  to  a  smooth 
edge,  or  with  any  suitable  tool.  These  divisions  may  be  painted  with 
a  very  narrow  brush. 

(c)  Weigh  the  rod. 

(d)  By  means  of  a  thread  fastened  to  a  loop  of  fine  wire  previously 
soldered  to  the  end  which  was  not  used  as  the  zero  of  graduation,  sus- 
pend the  rod  from  the  hook  in  the  bottom  of  one  of  the  scale  pans. 
It  should  hang  with  axis  accurately  vertical. 

(e)  Bring  the  balance  to  equilibrium,  and  arrest  the  beam.  Then 
bring  from  below  the  cylinder  of  water,  raising  it  slowly  until  about 
2  cm.  of  the  rod  are  submerged  (Fig.  97).  Support  the  cylinder  in 
this  position  by  blocks. 

(/)  Free  the  beam  of  the  balance  slightly,  and  readjust  by  adding 
weights  to  the  scale  pan  from  which  the  rod  hangs.  Note  the  amount 
thus  added  and  the  depth  of  submergence  of  the  rod  when  the  beam  is 
free  and  the  pointer  of  the  balance  is  at  zero. 

(g)  Raise  the  cylinder  by  steps  of  about  2  cm.  each,  repeating 
operation  (  /")  for  each  position,  until  complete  submergence  is  reached. 
Compute  the  mass  of  water  displaced  at  each  stage  of  the  determina- 
tion,1 and  compare  it  with  the  corresponding  masses  of  the  weights 
added  to  balance  the  buoyant  force  of  the  liquid.  Your  result  should 
accord  with  the  principle  of  Archimedes. 

(A)  Repeat  the  above-mentioned  measurements,  using  the  lighter 

1  One  cubic  centimeter  of  water  weighs  one  gram. 


THE  PROPEETIES   OF  LIQUIDS 


121 


rod.  From  the  final  step  of  this  experiment,  which  is  reached  when 
the  buoyant  force  entirely  supports  the  rod,  you  should  be  able  to 
deduce,  from  the  weights  added  and  the  weight  of  the  rod  in  air,  the 
following  law  of  floating  bodies,  viz. 

A  floating  body  displaces  its  own  weight  of  liquid. 


FIG.  97. 


122  THE  OUTLINES  OF  PHYSICS 


CHAPTER   XIII 

DENSITY 

106.  Application   of   the   Principle  of  Archimedes  to  the 
Measurement  of  the  Densities  of  Solids  and  Liquids.  —  The 
buoyant   force   upon   submerged   bodies   affords   some  of 
the  most  convenient  and  accurate  methods  of  comparing 
the  densities  of  both  solids  and  liquids.     The  basis  of  the 
comparison,  in  the  case  of  solids  and  liquids,  is  the  density 
of  water  ;  in  the  case  of  gases,  air  is  sometimes  taken  as 
the  standard   of   reference,  while  sometimes  hydrogen  is 
used  and  sometimes  water. 

107.  Density.  —  Density  is  defined  as  the  mass  per  unit 
volume.     The   formula  which  gives  the  relation  between 
these  three  quantities  is  accordingly 


in  which  D  is  the  density,  M  the  mass,  and  F"the  volume. 
In  the  comparison  of  the  densities  of  other  substances 
with  that  of  water,  the  term  specific  gravity  is  commonly 
used  to  express  the  result.     The  specific  gravity  S  is 


in  which  d  is  the  density  of  water  at  the  temperature  of 
the  experiment. 


DENSITY 


123 


108.    EXPERIMENT  27.  —  The  Measurement  of  Density  by  weigh- 
ing in  Air  and  in  Water. 

Apparatus  : 

(1)  A  balance  and  weights. 

(2)  A  beaker  of  water. 

(3)  A  block  of  metal  weighing  about  200  grams.1 
Procedure  : 

(a)  Suspend  the  body,  the  density  of  which  is  to  be  determined, 
from  the  hook  of  the  right-hand  scale  pan  and  find  its  weight. 
(/;)  Bring  the  beaker  of  water  into 
the  position  shown  in  Fig.  98,  so  as 
to  submerge  the  body,  and  weigh 
again.  The  loss  of  weight  in  water 
affords  a  measure  of  the  buoyant 
force  of  the  latter,  and  is  equivalent, 
as  we  have  already  seen,  to  the  weight 
of  the  water  displaced  by  the  sub- 
merged body.  The  ratio  of  the  weight 
in  air  to  the  loss  of  weight  in  water, 

weight  in  air          _      _  D 
loss  of  weight  in  water  d  ' 


for  the  mass  of  the  body  is  M  =  D  V, 
and  that  of  the  displaced  water  is 
m  =  d  V,  so  that 


FIG.  98. 


The  method  just  described  may  be 
used  to  determine  the  density  of  liquids  also.  In  that  case  a  body 
of  known  mass  and  density  is  submerged  in  the  liquid  the  density  of 
which  is  desired,  and  is  wreighed.  A  comparison  of  its  loss  of  weight 
in  that  liquid  and  in  water  gives  the  specific  gravity  of  the  former. 

1  It  is  desirable  to  use  for  this  experiment  a  solid  with  smooth  surface 
and  free  from  cavities  or  indentations.  When  it  is  necessary  to  find  the 
density  of  materials  of  rough  exterior,  or  porous,  they  should  be  sub- 
merged, and  the  vessel  of  liquid  containing  them  should  be  placed  under 
the  exhausted  receiver  of  an  air  pump,  until  the  air  entrapped  within  the 
interstices  of  the  material  is  set  free. 


124 


THE  OUTLINES   OF  PHYSICS 


109.  Method  of  the  Hydrometer.  —  The  fact  that  a  float- 
ing body  always  displaces  its  own  mass  of  the  liquid 
which  sustains  it,  is  made  use  of  in  the  hydrometer,  which 
is  an  instrument  designed  for  the  ready  approximate  indi- 
cation of  the  densities  of  liquids.  The  hydrometer  con- 
sists of  a  glass  float  of  the  form  shown  in  Fig.  99.  It  is 
ballasted  by  means  of  mercury  or  shot  in  the  bulb  6,  so 
that  it  will  rest  in  an  upright  position,  all  submerged 
excepting  a  portion  of  the  narrow  cylindrical 
stem.  The  extent  to  which  the  stem  itself 
will  be  submerged  depends  obviously  upon 
the  volume  of  liquid  necessary  to  equal  the 
hydrometer  in  mass.  Hydrometers  are  usu- 
ally constructed  with  a  scale  which  gives  the 
densities  directly  in  terms  of  that  of  water. 
If  the  instrument  is  to  be  used  in  liquids 
denser  than  water  it  is  ballasted  so  as  to 
float  almost  submerged  in  the  latter.  (See 
(1),  Fig.  99.)  With  increasing  density  of  the 
surrounding  liquid  the  stem  emerges  above 
the  surface  more  and  more.  For  use  in 
liquids  lighter  than  water  the  ballast  is  ad- 
justed so  that  the  hydrometer  will  float  in 
that  liquid  with  nearly  the  whole  of  the  stem  exposed. 
As  the  density  of  the  liquid  diminishes,  the  hydrometer 
sinks,  and  new  parts  of  the  scale  upon  the  stem  come  to 
the  surface. 

Many  special  forms  of  hydrometer  are  used  in  the  indus- 
trial arts,  and  these  possess  scales  convenient  to  their  various 
purposes.  Such  instruments  are  the  alcoholometer,  which 
indicates  directly,  by  the  depth  to  which  it  sinks,  the  per- 
centage of  alcohol  which  the  sample  of  spirits  in  which 
it  floats  contains;  the  salinimeter  and  acidimeter,  which 


FIG.  99. 


DENSITY 


125 


give  in  direct  readings  the  degree  of  concentration  of  brine 
or  the  strength  of  an  acid. 

110.  Hydrometers  of  Constant  Immersion.  —  All  of  the 
hydrometers  mentioned  in  Art.  109  have  a  common  prin- 
ciple of  action.  They  are  called  hydrometers  of  variable 
immersion.  Fahrenheit,  the  originator  of  the  type  of  ther- 
mometer which  goes  by  his  name,  devised  an  hydrometer, 
the  slender  neck  of  which  carries  but  one  mark.  The  instru- 
ment is  constructed  with  a  tiny  scale  pan  above  (Fig.  100), 


FIG.  100. 


FIG.  101. 


and  the  method  of  using  it  consists  in  placing  weights  upon 
the  pan  until  the  mark  coincides  with  the  level  of  the 
liquid.  The  mass  thus  added,  plus  the  mass  of  the  hy- 
drometer itself,  measures  the  mass  of  the  displaced  liquid. 
Nicholson  extended  the  usefulness  of  the  hydrometer  of 
constant  immersion  to  the  measurement  of  the  density 
of  solids.  The  Nicholson  hydrometer  (Fig.  101)  is  con- 
structed of  metal  instead  of  glass.  The  ballast  is  placed 
in  a  conical  vessel  below  the  float,  and  the  cover  of  this 


126  THE  OUTLINES   OF  PHYSICS 

vessel  serves  as  a  submerged  scale  pan.  The  method  of 
using  this  type  of  hydrometer  is  indicated  in  the  follow- 
ing experiment: 

111.  EXPERIMENT  28.  —  The  Measurement  of  Densities  with  the 
Nicholson  Hydrometer. 

Apparatus: 

(1)  The  hydrometer  and  a  set  of  weights  from  1  mg.  to  20  g. 

(2)  A  cylindrical  vessel  of  water ;  a  piece  of  metal,  or  glass,  or  a 
crystal  insoluble  in  water.     The  weight  of  the  specimen  should  be 
about  10  g. 

Procedure : 

(a)  Float  the  hydrometer,  and  add  weights  to  the  upper  scale  pan 
until  the  point  below  the  pan  touches  the  surface  of  the  water  ;  or  if 
the  instrument  be  one  of  the  form  with  a  single  upright,  until  the 
mark  coincides  with  the  surface.1 

(6)  Note  the  weights  upon  the  pan,  and  remove  them,  repeating 
the  count.  Place  the  specimen  upon  the  upper  pan,  and  add  weight 
sufficient  to  bring  the  point  again  into  contact  with  the  surface  film. 
Count  and  remove  the  weights  as  before.  The  difference  between  this 
weight  and  the  previous  one  is  the  weight  of  the  specimen  in  air. 

(c)  Place  the  specimen  upon  the  submerged  pan,  and  add  weights 
to  the  upper  pan  until  the  adjustment  is  restored.  The  difference 
between  this  weight  and  the  weight  used  in  operation  (a)  is  the 
weight  of  the  specimen  in  water. 

112.  Method  of  the   Specific   Gravity  Flask.  —  In   meas- 
uring the  density  of  fluids  it  is  not  necessary  to  have 
recourse  to  the  indirect  methods  based  upon  the  principle 
of  Archimedes.     Indeed  the  customary  method,  when  the 

1  The  instrument  here  described  is  a  modification  of  the  hydrometer  of 
Nicholson,  in  which  the  adjustment  is  made  by  means  of  a  pointer  pro- 
jecting downwards  from  the  middle  of  the  scale  pan.  This  device 
affords  a  much  more  delicate  and  definite  indication  of  the  depth  of  sub- 
mergence than  it  is  possible  to  get  with  a  mark  upon  the  neck  of  the 
hydrometer  as  found  in  the  original  form. 


DENSITY 


127 


FIG.  102. 


density  of  a  liquid  is  required  with  greater  accuracy 
than  that  easily  obtainable  with  the  hydrometer,  con- 
sists simply  in  weighing  a  flask  of  known 
volume  (and  of  known  mass  when  empty) 
which  has  been  filled  with  the  liquid  in 
question.  Such  a  vessel  is  called  a  specific 
gravity  flask.  It  is  commonly  given  the 
form  shown  in  Fig.  102,  and  consists  of  a 
bottle  of  thin  glass,  the  accurately  ground 
stopper  of  which  contains  a  capillary  open- 
ing, through  which  at  the  time  of  filling  the 
excess  of  liquid  may  escape.  In  the  case  of 
gases  the  procedure  is  analogous,  but  the 
flask  becomes  a  metal  globe  containing  several  liters  of 
gas,  and  provided  with  a  stopcock. 

113.   EXPERIMENT  29.  —  Density  of    Liquids  by  the   Method    of 
Liquid  Columns  (Hare's  Method). 

Apparatus : 

(1)  The  device  shown  in  Fig.  103,  which 
consists  of  two  long  straight  tubes  of  glass, 
terminating  beneath   the   surface   of  two 
beakers,  which  contain  the  liquids  to  be 
compared. 

The  upper  ends  of  the  tubes  are  con- 
nected together  and  to  the  air  pump  by 
means  of  the  "  T"  tube  (£)  and  connect- 
ing tubes  of  soft  rubber. 

(2)  Some   water,    alcohol,    solution    of 
brine,  oil,  mercury,  etc. 

(3)  An  air  pump. 

(4)  A  scale  divided  to  centimeters. 

Procedure : 

(a)  One  of  the  liquids  to  be  tested  is 

poured  into  one  of  the  beakers.      The  other  beaker  is  nearly  filled 
with  water. 


PUMP 


FIG.  103. 


128 


THE  OUTLINES   OF  PHYSICS 


(b)  The  pressure  within  the  tubes  is  reduced  (necessarily  by  like 
amount)  by  the  action-  of  the  air  pump,  whereupon 
the  atmospheric  pressure  upon  the  surface  of  the 
liquids  within  the  beakers  is  no  longer  balanced  by 
the  pressure  within  the  tubes,  and  drives  the  liquid 
upwards  in  each  of  these  to  a  height  inversely  pro- 
portional to  its  density.  (See  further  Chapter  XV, 
Properties  of  Gases.) 

The  liquid  columns  are  sustained  by  closing  b, 
which  is  a  pinchcock  of  the  well-known  form  shown 
in  Fig.  104.  The  experiment  consists  in  measuring 
the  heights  of  the  liquid  columns  thus  formed,  using 
substances  of  known  density,  which  should  have  been 

previously  determined  by  one  of  the  methods  already  described,  and 

verifying  the  statement  just  made. 


FIG.  104. 


114.  The  Density  of  Certain  Substances. 


TABLE. 
I.    THE  COMMON  ELEMENTS. 


Substance 
Aluminium 

Density 

2  56  to    2-80 
6-70  to    6-72 
9-76  to    9-93 
3-15 
2-17  to    2-32 
3-49  to    3-53 
8-30  to    8.70 
8-88  to    8-95 
19-30  to  19-34 

4-948 
7-03  to    7-73 

7-79  to    7-85 
7-60  to    7-80 
7-85  to    7-88 

Substance 
Lead  . 

Density 
11-20    to  11-45 

Antimony 

Magnesium 

1-69    to    1-75 

Bismuth 

Manganese  . 
Mercury    .  . 

....     7-10    to    8-03 
13-5958 

Bromine  

Carbon  {  (graPhi^)  - 
[  (diamond)  . 
Cobalt  .  .  . 

Nickel  .  . 

8-57    to    8-93 

Nitrogen 

0-001254 

Oxygen 

0-001429 

Copper  .  . 

Phosphorus  | 

Platinum  .  . 
Potassium 

(common)  1-836 
(red)       2-15  to  2-34 
....  21-2      to  21-7 
0-875 

Gold  . 

Hydrogen 

Iodine  

f  (cast)    

Silver  .  . 

.      .  .  10-42    to  10-57 

Iron  |  (wrought)  .  .  . 
1  (steel) 

Sodium 

.     .       0-978 

Sulphur  .  .  . 
Tin 

.  .  .  .     1-97    to    2-13 
6-97    to    7-37 

1  (pure)  . 

Zinc  . 

.    6-87    to    7-24 

DENSITY 


129 


II.    ^'rARIOus  MATERIALS. 


Anthracite    ......  1-40  to  1-80 

Asbestos 2-05  to  2-80 

Clay 1-80  to  2-60 

Glass 2-50  to  3-90 

Granite 2-50  to  2-90 

Ivory 1-80  to  1-90 

Marble 2-65  to  2-80 

Porcelain    .                 ,  2-24  to  2-49 


Beeswax 0-960  to  0-965 

Butter 0-865  to  0-868 

Gasoline 0-660  to  0-690 

Linseed  oil 0-930  to  0-935 

Milk  (cow's)  ....  1-028  to  1-035 

Palm  oil 0-905 

Paraffin 0-880  to  0-930 

Petroleum 

(refined)  250°  .  .  0-800  to  0-830 


130  THE  OUTLINES   OF  PHYSICS 


CHAPTER  XIV 

PROPERTIES   OF   THE   SURFACE   FILM   OF  LIQUIDS 

115  The  Surface  of  a  Liquid  is  Normal  to  the  Force  acting 
upon  it.  —  The  surface  of  a  liquid  at  rest  is  always  perpen- 
dicular at  each  point  to  the  resultant  force  acting  at  that 
point.  If  gravity  be  the  only  force,  the  surface  will  be 
level,  i.e.  at  right  angles  to  a  line  drawn  from  the  surface 
to  the  center  of  the  earth.  If  other  forces  act,  the  surface 
takes  other  forms,  but  always  in  accordance  with  the  above 
principles.  When  solids  and  liquids  come  into  contact,  the 
molecular  forces,  the  existence  of  which  between  solids 
and  liquids  has  been  demonstrated  in  Chapter  X,  produce 
easily  observable  modifications  of  the  form  of  the  surface. 

A  glass  vessel  of  water 
partly  filled  presents 
the  appearance  of  Fig. 
105,  the  liquid  rising 
on  every  side  to  meet 
the  glass.  If  water  be 

FIG.  105.  FIG.  100.  ji     i-        i         i    T    i  ,1 

added  to  a  level  slightly 

above  the  lip  of  the  glass,  the  molecular  forces  prevent 
outflow.  The  excess,  which  may  be  plainly  seen  in  a  flat 
dome  above  the  vessel,  is  held  in  position  by  the  surface 
layer  of  the  liquid,  the  particles  of  which  are  locked 
together  so  as  to  form  a  film  or  skin. 

Mercury  in  a  glass  vessel  shows  analogous  phenom- 
ena save  that  the  surface  is  convex  instead  of  concave 


SURFACE  FILM  OF  LIQUIDS 


131 


(Fig.  106).    The  film  in  the  latter  case  does  not  make 
molecular  contact  with  the  glass,  but  shrinks  away  from  it. 

The  surface  of  a  liquid  contained  in  a  vessel  will  be 
concave  whenever  the  liquid  wets  the  containing  vessel ; 
that  is  to  say,  whenever  the  molecular  forces  between 
the  solid  and  liquid  exceed  those  between  neighboring 
particles  of  the  liquid.  It  will  be  convex  whenever  the 
molecular  forces  between  the  liquid  particles  are  in  excess. 
„  Analogous  deformations  of  the  surface  occur  wherever 
solids  and  liquids  are  brought  into  contact.  If  a  glass  rod 
be  brought  into  con- 
tact with  water  from 
above,  the  liquid  film 
rises  along  the  sur- 
face of  the  glass,  and 
the  rod  may  be  raised 
above  the  general 
level,  lifting  with  wwtf^wmmww^ 
it,  by  virtue  of  the  FJG-  107- 

strength  of  the  surface  film,  a  considerable  volume  of  liquid 
(see  Fig.  107). 

When  such  a  point  impinges  upon  mercury,  the  film 
bends  under  it  so  that  a  cavity  is  formed  within  which  the 
end  of  the  rod  lies  be- 
low the  general  level 
of  the  mercury,  but 
not  within  the  mass 
of  the  liquid  itself 
(Fig.  108). 

Even   if   the   rod 
be  plunged  to  great 
depth  below  the  level  of  the  mercury,  there  will  be  no  true 
junction  between  the  glass  and  the  liquid  like  that  which 


FIG. 108. 


132 


THE  OUTLINES   OF  PHYSICS 


exists  between  glass  and  the  water  in  which  it  is  submerged. 
The  surface  film  will  still  separate  the  body  of  the  liquid 
from  the  glass,  and  a  thin  layer  of  air  will  remain  between 
the  two  substances. 

If  open  tubes  be  plunged  into  any  liquid,  this  same  action 
of  the  surface  film  produces  either  a  rise  in  the  level  of  the 
liquid  within  the  tube  (Fig.  109)  where  the  surface  is  con- 
cave, or  a  corresponding  depression  (Fig.  110)  where  the 
surface  is  convex. 

In  tubes  of  small  bore  the  rise  is  very  noticeable  ;  whence 
the  name  capillarity,  which  has  been  extended  to  all  the 
phenomena  depending  upon  the  action  of  the  surface  film. 

116.  The  Law  of  Diameters.  —  The  rise  or  depression  of 
liquid  in  tubes,  measured  from  the  general  level  of  the 
surrounding  liquid,  is  inversely  proportional  to  the  diameter 
of  the  tube. 


FIG. 109. 


FIG.  110. 


117.  Theory  of  the  Surface  Film.  —  The  reason  for  as- 
cribing these  phenomena  to  action  of  a  surface  film  is  as 
follows :  Consider  any  particle  within  the  body  of  a  liquid. 
If  it  is  far  below  the  surface,  the  molecular  forces  due 
to  the  surrounding  particles  will  be  the  same  in  all  direc- 
tions. If,  however,  the  particles  lie  close  to  the  surface, 
as  in  Fig.  Ill,  where  m  is  the  particle,  and  r  is  the  radius 
of  the  sphere  within  which  the  action  of  the  molecular 


SURFACE  FILM  OF  LIQUIDS 


133 


forces  is  appreciable,  there  will  be  forces  due  to  particles 
immediately  below  m,  which  are  not  counterbalanced  by 

forces   from   above,  owing  ^ v 

to  the  proximity  of  the 
surface.  The  resultant  of 
all  these  unbalanced  forces 
is  inwards  at  right  angles 


•t' 


FlG.   111. 


to  the  surface,  and  the 
resultants  which  exist  in 
the  case  of  all  the  liquid  particles  near  the  surface,  con- 
stitute a  pressure  normal  to  the  surface  exerted  by  the 
particles  which  form  the  surface  layer  (or  film)  upon  the 
body  of  the  liquid  within. 

It  is  evident  that  this  pressure  will  be  greater  in  the 
case  of  a  convex  film  (Fig.  112),  and  less  in  the  case  of  a 
concave  film  (Fig.  113),  than  in  that  of  plane  film. 


FIG.  112. 


FIG.  113. 


The  cause  of  the  rise  or  depression  of  liquids  in  capil- 
lary tubes  obviously  lies  in  the  curvature  of  the  surface 
film.  The  pressure  exerted  by  a  plane  film  is  capable  of 
driving  liquid  above  the  general  level  in  tubes  which  the 
liquid  wets,  because  the  film  which  caps  the  liquid  in  such 
tubes  is  concave.  When,  on  the  other  hand,  the  film  is 
convex,  which  is  the  case  when  the  solid  is  not  wet,  the 
film  is  stronger,  and  it  depresses  the  liquid  below  the  gen- 
eral level,  as  already  described. 


134 


THE   OUTLINES   OF  PHYSICS 


FIG.  114, 


118.  Angle  of  Contact.  —  The  curvature 
of  the  liquid  film  in  the  neighborhood  of 
solids  depends,  as  has  already  been  shown 
(Art.  115),  upon  the  relative  strength  of 
the  molecular  forces  within  the  liquid  and 
between  liquid  and  solid.  This  relation 
determines  the  angle  of  contact,  by  which 
the  capillary  behavior  of  liquids  in  various 
containing  vessels  may  be  defined.  This 
is  the  angle  «,  Fig.  114,  which  the  film 
makes  with  the  solid  wall  at  the  point  of 
contact.  The  angle  may  be  greater,  equal 
to,  or  less  than  90° 

In  the  first  case  there  will  be  depression, 
in  the  last  elevation^  in  capillary  tubes. 


119.    EXPERIMENT  30.  —  Van  der  Mensbrugghe's  Experiment  show- 
ing that  a  Liquid  Film  is  always  under  Tension. 

Apparatus  : 

(1)  A  wire  ring  about  10  cm.  in  diameter,  within  which  hangs  a 
loop  of  thread  as  shown  in  Fig.  115. 

(2)  A  dish  containing  a  soap  solution. 


FIG 


Procedure  : 

(a)  Dip  the  ring  into  the  solution,  whence  it  emerges  carrying  a 
plane  soap  film  bounded  by  the  ring  and  completely  filling  it.  The 
loop  of  thread  may  be  seen  floating  in  the  liquid  layer  within  which 


SURFACE  FILM  OF  LIQUIDS 


135 


it  moves  freely,  excepting  as  it  is  constrained  by  the  strand  which 
connects  it  with  the  ring. 

(b)  The  film  consists  of  two  distinct  regions :  that  outside  of  the 
loop  of  thread  and  that  within  the  loop. 

Puncture   the    latter  region   with   any  con- 
venient tool,  such  as  a  pin  or  needle  or  a  bit 
of  wire.     The  result,  which  follows  instantly, 
is  most  beautiful  and  striking.     The  thread, 
hitherto  lax,  is  drawn  into 
circular  form  by  the  tensile 
forces  of  the  outer  region  of  the  film  which 
are  no  longer  balanced  by  those  of  the  region 
within  the  loop.     It  is  now  held  tensely  to 
its    position   of    equilibrium  within  the  film 
(Fig.  116),  and  its  laxity  and  freedom  of  motion  have  disappeared. 

If  the  ring  used  in  this  experiment  be  mounted  in  the  field  of  a 
lantern,  this  phenomenon  can  be  exhibited  to  many  observers  simul- 
taneously 

120.    EXPERIMENT  31.  —  Contractile  Power  of  a  Water  Film. 

Ernest  Mchols  has  extended  the  principle  of  Van  der  Mensbrugghe's 
experiment  to  the  study  of  the  surface  film  of  a  body  of  water.  In 


FIG.  116. 


FIG.  117. 


this  form  of  the  experiment  an  ordinary  rubber  band,  of  the  oblong, 
slender  form  used  to  hold  packages  of  postal  cards,  etc.,  together,  is 
made  to  float  upon  the  surface  of  water  (Fig.  117). 

The  inner  region  of  the  film,  that,  namely,  which  is  bounded  by 
the  loop  of  caoutchouc,  is  then  touched  with  a  wire  or  splinter  of 
wood  which  has  been  dipped  into  alcohol  or  oil.  The  result  is  to  alter 


136 


THE   OUTLINES   OF  PHYSICS 


the  angle  of  contact  and  with  it  the  tension  of  the  film.  The  outer 
region,  still  uncontaminated,  exerts  in  full  its  previous  pull  upon  the 
loop,  and  these  forces,  no  longer  balanced  by  those  from  within,  dis- 
tend the  band  into  the  form  shown  in  the  figure.  The  application  of 
a  trace  of  the  alcohol  or  oil  to  the  outer  region  will  instantly  restore 
the  band  to  its  original  lax  position  and  shape. 


FIG.  118. 


121.   EXPERIMENT  32.  —  Contractile  Tendency  of  the  Soap  Bubble. 

Apparatus  : 

A  glass  funnel  about  8  cm.  in  diameter  at  the  mouth,  some  soap 
solution,  a  lighted  candle. 

The  soap  bubble  consists  of  a  layer  of  liquid  the  outer  film  of 
which,  being  convex,  must  always  exert  a  greater  pressure  than  does 

the  inner  concave  film.    There  is  there- 
fore a  resultant  pressure  tending  to  ex- 
pel the  contained  air  from  the  bubble 
and  to  reduce  the  size  of  the  latter. 
Procedure : 

Blow  a  bubble  with  the  above  ap- 
paratus, and  hold  the  open  tip  of  the 
funnel  horizontally  near  the  candle 
flame,  as  in  Fig.  118.  The  outflow 
will  be  found  sufficient  to  distort  and 
almost  to  put  out  the  flame. 

Note  that  this  effect  does  not  cease  when  the  soap  film  reaches  the 
mouth  of  the  funnel,  but  that  the  film  continues  to  move  toward 

the  apex,  driving  the  air  before 
it.  This  tendency  to  recede  into 
the  part  of  the  funnel  which 
has  the  least  diameter  is  due  to 
the  difference  in  curvature  of 
the  two  films  which  inclose  the 
liquid  layer  (Fig.  119).  The  re- 
sultant pressure  is  always  in- 
ward. Where  the  angle  between 
opposite  walls  is  considerable, 
FIG.  119.  ^e  f°rce  is  sufficient  to  lift  the 

layer  bodily  against  gravity. 

This  statement  should  be  verified  by  turning  the  tip  of  the  funnel 
upwards  and  observing  the  behavior  of  the  soap  film. 


PROPERTIES   OF  GASES  137 


CHAPTER   XV 
PROPERTIES   OF   GASES 

122.  Definition  of  a  Gas.  —  Gases  differ  from  liquids  in 
not  having  a  surface  film.     There  is  much  greater  freedom 
of  motion  between  the  particles,  and  the  molecular  forces 
do  not  produce  the  same  degrees  of  constraint  as  in  the 
case  of  solids  and  liquids.     When  subjected  to  pressure, 
liquids   change    volume    but    slightly   (water  under    265 
atmospheres  of   pressure    loses   only  about   yol5in>    °^   ^s 
original  volume).     Gases,  on  the  other  hand,  are  freely 
compressible. 

123.  Boyle's  Law  (Mariotte's  Law).  —  The  relation  be- 
tween volume  and  pressure  in  the  case  of  gases  is  a  per- 
fectly definite  and  very  simple  one,  and  it  is  the  same  for 
all  gases.     It  was  announced  by  Boyle  (1662)  and  inde- 
pendently by  Mariotte  (1679),  and  is  as  follows: 

The  volume  of  a  gas  varies  inversely  as  the  pressure  to 
which  it  is  subjected. 

The  equation  _2  =  — -1, 

in  which  Vl  and  V^  are  the  volumes  of  a  given  body  of 
gas  at  pressures  Pl  and  P2  respectively,  is  a  statement 
of  Boyle's  law. 

124.  EXPERIMENT  33.  —  Measurement  of  the  Mass  of  a  Gas. 

Apparatus : 

(1)  A  thin-walled  brass  sphere  containing  about   1000  cc.,  with 
stopcock  threaded  to  fit  the  air  pump  (such  spheres  are  usually  fur- 


138 


THE  OUTLINES   OF  PHYSICS 


nished  as  accessories  to  that  instrument,  and  afford  the  best  apparatus 
for  this  experiment). 

(2)  An  air  pump. 

(3)  A  balance  and  weights. 
Procedure : 

(a)  Weigh  the  receptacle  filled  with  air ;  then  exhaust  upon  the 
air  pump,  close  the  stopcock,  and  weigh  again.     Note  the   marked 
diminution  of  mass  due  to  the  absence  of  gas  which  the  receptacle 
contained  when  first  weighed.     (This  would  amount  to  1-3  grains  per 
liter  in  case  the  exhaustion  were  complete.) 

(b)  After  weighing  again,  attach  the  receptacle  to  a  gas  jet  by 
means  of  a  rubber  tube,  open  the  stopcock,  and  turn  on  the  gas. 
(The  gas  should  have  been  on  previously  for  a  second  or  two  and 
allowed  to  escape,  so  as  to  free  the  pipes  from  air.)     Turn  off  the 
gas,  close  the  stopcock,  detach  the  receptacle,  and  weigh  again.     Note 
that  there  is  increase  over  the  mass  of  the  empty  receiver,  but  that 
the  weight  is  decidedly  less  than  when  filled  with  air.     If   carbon 
dioxide,  nitrous  oxide,  or  hydrogen,  in  cylinders,  are  accessible,  the 
receptacle  may  be  exhausted  and  filled  with  these  also  and  weighed. 

Accurate  measurements  of  the  density  of  gases  cannot  be  expected 
with  the  apparatus  described  above.  The  various  weighings  should, 
however,  indicate  densities  relatively  of  the  same  order  as  those  given 
in  the  following  table. 

TABLE. 

DENSITY  OF  CERTAIN  GASES  AT  76  CM.  PRESSURE  AND  0°  C.  (EXPRESSED 
IN  GRAMS  PER  LITER). 


Gas. 

Density  com- 
pared with  air. 

Mass  in  grams 
per  liter. 

Air 

1-0000 

1-2934 

Carbon  monoxide  (CO)  
Carbon  dioxide  (C02)      

0-9671 
1-5198 

1-2505 
1-9651 

Chlorine  (C12) 

2-4495 

3-1674 

Hydrogen  (H2)  . 

0-0692 

0-0895 

Methane  (marsh  gas)  (CH4)  .... 
Nitrogen  (N2)      
Nitrous  oxide  (N20) 

0-5530 
0-9702 
1-5229 

0-7150 
1-2546 
1-9692 

Oxygen  (02)  

1-1053 

1-4292    - 

Illuminating  gas 

0-4:38  ± 

0-566  ± 

PROPERTIES   OF  GASES  139 

125.  Extension  of   the   Principle   of   Pascal   to   Gases.  — 
Since  a  gas  is  a  perfect  fluid,  it  transmits  pressure,  and 
when  it  is  at  rest  the  pressures  at  any  point  within  it 
are  always  the  same  in  every  direction.     (Consider   the 
spherical  form  of  soap    bubbles  in  still  air  as  a  delicate 
proof  of  this  statement.) 

Since  gases  have  mass,  however,  pressures  must  increase 
from  above  downwards,  owing  to  the  action  of  gravity ; 
the  pressure  at  any  level  being  that  due  to  the  weight  of 
the  superincumbent  column  of  gas.  It  is  possible,  by 
means  of  a  device  due  to  the  Italian  physicist,  Torricelli 
(1644),  who  was  a  disciple  of  Galileo,  to  show  the  exist- 
ence of  this  pressure  in  the  case  of  the  earth's  atmosphere, 
and  to  measure  the  amount  of  it. 

126.  Torricelli's    Experiment.  —  Torricelli    filled    glass 
tubes  closed  at  one  end  with  mercury,  and  inverted  them 
in  a  cistern  of  the  same  liquid. 

He  found  that  when  the  tube  had  a  length  of  less  than 
about  76  cm.,  in  the  case  of  an  experiment  performed  at 
the  level  of  the  sea  (a,  Fig.  120),  or  when  it  was  so 
inclined  that  the  vertical  height  above  the  level  of  the 
cistern  (6,  Fig.  120)  was  less  than  76  cm.,  the  tube 
remained  full.  The  mercury  which  it  contained  was 
held  in  place  by  the  atmospheric  pressure  upon  the  sur- 
face of  the  cistern.  When,  however,  the  tube  rose  to  a 
greater  height  than  the  above  (<?,  Fig.  120),  the  mercury 
receded  in  the  tube,  and  came  to  rest  in  such  a  position 
that  the  column,  sustained  above  the  general  level  of  the 
cistern,  precisely  balanced  the  atmospheric  pressure.  This 
occurs,  as  indicated  above,  when  the  column  has  a  vertical 
height  of  about  76  cm.  The  amount  varies  slightly  in  a 
given  locality  from  time  to  time  through  a  range  of  sev- 
eral centimeters. 


140 


THE  OUTLINES   OF  PHYSICS 


Torricelli's  apparatus  affords  the  most  direct  and  satis- 
factory means  of  measuring  atmospheric  pressure.  When 
used  for  this  purpose  it  is  known  as  the  mercury  barometer. 


FIG.  120. 

127.  Construction  of  the  Barometer.  —  In  order  that  Tor- 
ricelli's apparatus  may  serve  as  an  instrument  of  precision, 
certain  conditions  have  to  be  very  carefully  fulfilled. 

(1)  The  mercury  must  be  pure  and  clean. 

(2)  The  vacuum  above  the  mercury  must  be  as  nearly 
as  possible  complete ;  i.e.  free  from  air,  aqueous  vapor,  etc. 

(3)  The  bore  of   the   tube  must  be  so  large  that  the 
depression  of  the  column,  due  to  the  action  of  the  surface 
film,  will  be  inappreciable,  or  the  diameter  must  be  known, 
and  a  correction  for  the  depression  must  be  applied. 

The  first  condition  is  attained  by  distilling  the  mercury 


PROPERTIES   OF  GASES 


141 


before  placing  it  in  the  tube ;  the  second,  by  boiling  the 
mercury  in  the  tube  before  inverting  it  in  the  cistern, 
thus  driving  off  all  gases  and  moisture. 

Barometers  are  provided  with  a  scale  by  means  of  which 
the  height  of  the  top  of  the  mercury  column,  above  the 
level  of  the  mercury  in  the  cistern,  may  be  read  in  centi- 
meters and  decimal  parts  of  a  centimeter  (or  in  countries 
where  the  British  system  of  measurement  is  used,  in  inches 
and  fractions  of  an  inch). 

In  order  to  maintain  the  mercury  in  the  cistern  at  a  con- 
stant level,  the  latter  is  commonly  provided 
with  a  flexible  bottom  of  leather  which  can 
be  raised  and  lowered  by  means  of  a  screw 
from  below  (Fig.  121),  and  with  a  pointer 
the  apex  of  which  is  rigidly  adjusted  to 
the  zero  point  of  the  scale.  Before  mak- 
ing a  reading  the  mercury  is  raised  until 
its  surface  makes  contact  with  the  pointer. 

Barometers  thus  arranged  are  known  as 
Fortin  barometers. 

Sometimes  barometers  are  given  the 
form  shown  in  Fig.  122,  in  which  a  bent 
tube,  with  one  open  and  one  closed  arm,  is 
filled  with  mercury.  In  this  case  the  dif- 
ference in  the  height  of  the  two  mercury 
columns  indicates  the  pressure,  and  there 
is  no  correction  for  capillary  depression. 


FIG.  121. 


128.  Nature  of  the  Atmosphere.  —  From  the  phenome- 
non presented  by  the  barometric  column  certain  important 
conclusions  may  be  drawn  concerning  the  constitution 
of  the  atmosphere.  A  layer  of  air  everywhere  of  the 
same  densitv  as  the  atmosphere  at  the  level  of  the  sea, 


142 


THE  OUTLINES   OF  PHYSICS 


and  capable  of  sustaining  a  mercury  column  76  cm.  high 
against  gravity,  would  need  to  have  a  height  H,  such  that, 

H:  h  :  :  dm  : 


where  h  is  the  height  of  the  mercury  column, 
dm  is  the  density  of  mercury,  and  da  is  the  den- 
sity of  air  at  76  cm.  pressure.  Now  1  cc.  of 
mercury  weighs  13.596  grams,  and  1  cc.  of  air 
at  the  same  temperature  (0°)  weighs  0-001293 
gram. 

The  value  of  77"  is,  therefore, 


=  4'95  miles  nearly. 

The  air  being  a  compressible  fluid,  however, 
does  not  lie  in  a  layer  of  uniform  density  en- 
veloping the  earth,  but  diminishes  rapidly  in 
density  from  the  surface  upwards.  There  is 
FIG.  122.  abundant  evidence  of  the  existence  of  atmosphere 
at  much  greater  heights  than  the  above.  Indeed, 
direct  observations  with  the  barometer  have  been  made  by 
aeronauts  at  a  height'  of  9600  meters  =  31,500  ft.,1  and 
there  are  reasons  to  think  that,  for  at  least  fifty  miles 
above  the  surface  of  the  earth,  there  is  an  appreciable 
atmosphere. 

1  At  that  distance  above  the  sea  the  barometric  column  was  less 
than  23  cm.  long.  Life  could  be  sustained,  even  temporarily,  only  by 
supplementing  the  scanty  supply  of  air  by  inhalations..  of  oxygen  from  a 
Cylinder  of  the  compressed  gas  provided  for  such  an  emergency.  (See 
account  of  the  ascent  made  by  Dr.  Berson,  Dec.  4,  1894  ;  Nature,  Vol.  51, 
p.  491.) 


PROPERTIES   OF  GASES 


143 


129.  Manometers. — The  barometric  column  may  also 
be  used  to  measure  changes  of  pressure  artificially  pro- 
duced. If,  for  example,  the  cistern  of  a  barometer  be 
placed  upon  the  plate  of  an  air  pump  with  the  tube  pro- 
jecting through  the  neck  of  the  receiver,  as  shown  in 
Fig.  123,  we  can  reduce  the  pressure  upon  the  surface  of 
the  cistern  at  will.  Every  stroke  of  the  pump  will  then 
lower  the  mercury  column  until  the  minimum  pressure  is 
reached. 


FIG.  123. 


FIG.  124. 


To  any  such  device  for  measuring  artificial  pressures,  the 
name  manometer  is  applied. 

For  the  measurement  of  pressures  less  than  one  atmqs- 
phere,  the  form  of  manometer  shown  in  Fig.  124  is  fre- 
quently used.  It  is  a  barometer  in  .which  the  vacuum 
above  the  mercury  column  is  variable. 

Where  pressures  both  greater  and  less  than  one  atmos- 
phere are  to  be  measured,  the  open  tube  manometer  (Fig. 


144 


THE   OUTLINES   OF  PHYSICS 


125)  is  employed.  The  difference  of  level  (/^2)  of  the 
mercury  in  the  two  arms  indicates  the  amount  (+  or  — ) 
by  which  the  pressure  varies  from  one  atmosphere. 

For  pressures  so  great  that  an  open  tube  manometer 
would  be  of  inconvenient  length,  the  end  of  the  tube  is 
sealed  as  in  Fig.  126,  and  advantage  is  taken 
of  the  compressibility  of  air  (see  Boyle's  law) 
to  secure  a  manometer  of  compact  form.  To 
this  type  the  name  closed  tube  manometer  is 
given. 

Sometimes,  finally,  the  bending  of  the 
flexible  top  of  a  metal  capsule  or  box,  or  the 
distortion  of  a  curved  and  flexible  tube  to 
which  pressure  is  applied,  is  magnified  me- 
chanically, giving  motion  to  a  pointer  which  moves  along 
a  dial.  This  principle  is  applied  to  barometers  (aneroid 


FIG.  126. 


FIG.  127. 


FTG.  128. 


barometers)  and  to  pressure  gauges.  The  stiffness  of  the 
moving  part  is  adapted  in  each  case  to  the  pressures  which 
it  is  intended  to  indicate. 

Figures  127  and  128  show  the  essential  features  of  two 
well-known  forms. 


PROPERTIES  OF  GASES 


145 


130.  EXPERIMENT  34.  — Measurement  of  the  Vacuum  produced  by 
a  Mechanical  Air  Pump,  and  Determination  of  the  Rate  of  Leakage  of 
the  Pump  and  Receiver. 

Apparatus  : 

(1)  An  air  pump  with  open  neck  receiver. 

(2)  A  wooden  scale  divided  to  centimeters ;  a  watch  or  other  time- 
piece. 

(3)  A  barometer. 


FIG.  129.     - 

Procedure : 

(a)  Bend  a  piece  of  glass  tubing,  about  120  cm.  long  and  0-5  cm. 

inner  diameter,  so  as  to  form  a  manometer  of   the  form  shown   in 

Fig.  124.     Fit  the  short  arm  to  the  neck  of  the  receiver  with  a  good 

cork   or   rubber  stopper.      Mount  the  receiver,  with  its  manometer 

L 


146 


THE  OUTLINES   OF  PHYSICS 


tube,  upon  the  plate  of  the  air  pump.  Bring  a  flat  dish  of  mercury 
from  below,  raising  it  until  the  open  lower  end  of  the  manometer  is 
well  submerged  and  supporting  it  in  position  with  blocks.  Set  up 
the  scale  vertically  with  its  edge  touching  the  tube,  the  lower  end 
of  the  scale  submerged  in  the  mercury  of  the  cistern  (Fig.  129). 


70cm. 


60cm. 


60cm. 


Le 

aka 

ye  c 

f 

\ 

A 

an 

_r_pi 

imp 

\ 

\ 

\ 

N 

Ul 

o: 

> 

\ 

Ul 

QC 
QL 

\ 

\ 

NS 

\. 

X 

X 

\ 

Til 

/IE 

100  s.                                300  s. 
FIG.  130. 

(6)  Take  fifty  strokes  with  the  pump,  timing  them  to  about  two- 
second  intervals.  Ten  seconds  after  the  last  stroke  read  the  position 
of  the  mercury  in  manometer  column.  Immediately  thereafter  note 
the  height  to  which  the  mercury  in  the  cistern  stands  upon  the  scale. 
Every  30  seconds,  for  at  least  5  minutes  after  the  first  reading  of  the 
height  of  the  manometer  column,  repeat  that  reading.  (If  the  leak- 
age is  so  rapid  as  to  render  readings  uncertain,  apply  beeswax.) 


PROPERTIES   OF  GASES 


147 


The  rate  of  leakage  will  vary.  Occasionally  the  loss  of  vacuum 
will  be  too  slow  to  give  marked  change  within  the  lime  assigned  to 
the  readings.  In  such  a  case  readings  may  be  made  at  longer 
intervals. 

(c)  Read  the  barometer,1  and  convert  the  readings  into  centi- 
meters if  necessary. 

(<l)  From  these  data,  which  should  be  tabulated  as  below,  find 
graphically  the  pressure  at  the  completion  of  the  last  stroke.  For 
this  purpose  construct  a  curve  with  times  as  abscissas  and  manometer 
readings  as  ordi nates.  This  curve  can  be  drawn  backwards  so  as 
to  cut  the  line  corresponding  to  0  seconds  (or  to  the  time  of  the 
last  stroke).  The  ordinate  at  that  point  is  the  required  value.  (See 
Fig.  130.) 

TABULATION  OF  DATA. — EXPERIMENT  34. 


Times  of 

observation. 

Time  after 
60th  stroke. 

Manometer 
reading. 

Height  of 
column.2 

li.           in.            8. 

sec. 

4        30        10 

10 

70-0 

08-7 

"        30        40 

40 

06-8 

65-5 

"        31        10 

70 

63-9 

62-6 

31        40 

100 

61-2 

.    59-9 

"        32        10 

130 

58-5 

67-2 

32        40 

160 

65-4 

54-1 

33        10 

190 

53-3 

62-0 

33        40 

220 

61-7 

50-4 

"         34         10 

250 

49-7 

48-4 

34        40 

280 

47-5 

46-2 

1  In  case  no  barometer  is  available,  assume  the  height  to  be  76  cm.  and 
use  that  value  in  subsequent  computation.     There  will  be  a  systematic 
error  in  values  for  the  vacuum,   equal   to  the   difference   between  the 
assumed  and  the  true  barometric  height. 

2  Obtained  by  subtracting  the  height  of  the  mercury  in  the  cistern 
above  the  zero  of  the  scale  ;  i.e.  1*3  cm. 

Barometer  reading,  74-3  cm. 

The  curve  corresponding  to  these  readings  (Fig.  130),  when  extended 
to  the  ordinate  for  0  sec.,  gives  for  the  initial  height  70-5  cm.  The  pres- 
sure was  therefore  reduced  to  74'3  —  70-5  =  3-8  cm. 


PART   II  — HEAT 


CHAPTER   XVI 

NATURE   AND  EFFECTS   OF  HEAT 

131.  Heat  is  the  name  given  to  a  form  of  energy  due  to 
some  motion  of  the  particles  of  a  body  among  themselves, 
and  not  of  the  body  as  a  whole.1 

Of  the  various  effects  of  heat,  which  we  shall  have 
occasion  to  consider,  one  of  the  most  general  is,  to  increase 
the  temperature  of  the  body.  This  increase  of  tempera- 
ture is  usually  accompanied  by  expansion. 

For  the  purpose  of  indicating  the  condition  of  a  body 
with  respect  to  heat  energy,  also  the  changes  as  loss  or 
gain  of  heat  which  it  undergoes,  the  above  effect,  i.e.  the 
increase  in  length  or  in  volume,  is  the  one  chiefly  em- 
ployed. This  effect  is  illustrated  by  means  of  the  follow- 
ing experiments. 

132.  EXPERIMENT  35.  —  Expansion  of  a  Bar. 

Apparatus :  (1)  A  bar  of  brass  or  iron  about  50  cm.  long,  and  mounted 
as  shown  in  Fig.  131.  The  supports  sl  and  s2  are  strips  of  sheet  metal 
cut  out  in  V  form  to  receive  the  bar,  and  fastened  to  wooden  blocks. 


FIG.  131. 

1  See  Elements  of  Physics,  Vol.  I,  p.  151,  introductory  remarks  con- 
cerning heat, 

148 


NATURE  AND  EFFECTS   OF  HEAT 


149 


FIG.  133. 


(2)    A  small   plane   mirror.      This   is  fastened  to  a  metal   disk 
(Fig.  132),  across  the  back 
of  which  is  soldered  a  thin 

strip  of  steel,  or  of  spring      .      „ 

brass,  about   O2  cm.  wide 
and  8  cm.  long.   Just  below  FlG- 132- 

the  center  of  this  strip,  and  touching  the  edge  of  it,  a  metal  pin  p 
(Fig.  131)  is  inserted,  or  is  soldered  to  the  disk.  The  ends  of  the 
metal  strip  are  tacked  to  the  arms 
of  a  wooden  yoke,  between  which  the 
mirror  swings  (Fig.  133),  and  this 
in  turn  is  clamped  to  a  wooden  block 
at  such  height  that  the  pin  will  coin- 
cide nearly  with  the  axis  of  the  bar, 
the  expansion  of  which  is  to  be 
measured. 

Procedure : 

(a)  The  bar  is  mounted  with  one 
end  in  contact  with  the  tack-head 
(Fig.  131).  The  block  carrying  the  yoke  and  mirror,  m,  is  then 
brought  into  position  at  the  other  end  of  the  bar  and  adjusted  until 
the  pin,  which  is  parallel  to  the  axis  of  the  bar,  is  in  firm  contact 
with  the  end  of  the  latter. 

(6)  A  beam  of  light,  either  of  sunlight  directed  by  means  of  a 
mirror,  or  the  rays  from  a  projecting  lantern,  is  thrown  obliquely 
upon  the  mirror  m,  and  thence  to  screen.  This  arrangement  of  the 
apparatus  once  perfected,  every  increase  in  the  length  of  the  bar  will 
tip  the  mirror  and  move  the  spot  of  light  along  the  screen. 

(c)  The  bar  is  heated  by  passing  the  flame  of  a  Bunsen  burner, 
held  in  the  hand  of  the  experimenter,  back  and  forth  between  the 
supports  Sl  and  S2.  The  movement  of  the  spot  of  light  which  follows 
this  heating  is  observed.  Note  that  the  direction  of  the  motion  is 
that  which  corresponds  to  an  elongation  of  the  bar.  (With  the 
above  described  arrangement  of  the  apparatus,  the  bar  in  cooling  will 
not  return  to  its  original  position,  a  fact  which  in  no  way  interferes 
with  the  success  of  the  experiment.) 

133.  Expansion  of  Liquids.  —  In  the  study  of  the  expan- 
sion of  liquids  various  indirect  methods  are  employed. 


150 


THE   OUTLINES   OF  PHYSICS 


FIG.  134. 


To  demonstrate  merely  the  fact  of  expansion,  the  follow- 
ing device  suffices : 

A  glass  bulb,  b  (Fig.  134),  is  filled  with  some  liquid 
(glycerine,  oil,  mercury,  or  water),  until  the  contents  rise 

part  way  into  the  long  neck. 

i       Around  the  neck  is  placed  a 
small  ring  of  rubber,1  which  is 
to  serve  as  a  mark  of  the  height 
at  which  the  liquid  stands. 
The   bulb  is   plunged   in  a 
vessel  of  cold  water,  where  it 
remains  for  several  minutes. 
The    ring    is    slipped    into 
HOT        place  to  mark   the   height   of 

'   the    liquid,   and    the   bulb   is 

transferred  to  a  vessel  of  hot 
water.  The  rise  of  the  liquid  within  the  neck  indicates 
not  only  that  the  liquid  expands  with  heat,  but  also  that  it 
expands  more  rapidly  than  does  the  containing  vessel. 

The  experiment  is  really  a  demonstration  of  what  is 
termed  the  relative  expansion  of  a  liquid.  When  the  con- 
taining vessel  expands  more  rapidly  with  rise  of  tempera- 
ture than  the  contained  liquid  does,  the  relative  expansion 
is  negative.  With  few  exceptions,  however,  liquids  expand 
more  rapidly  then  solids. 

134.  Absolute  Expansion  of  Liquids,  —  To  obtain  the  ex- 
pansion of  a  liquid,  independently  of  the  expansion  of  the 

1  Another  marker,  which  is  easily  constructed,  consists  of  a  strip  of 
sheet  iron,  the  length  of  which  is  slightly  less  than  the  outer 
circumference  of  the  neck  of  6.  If  this  be  rolled  into  a 
ring  (Fig.  135),  it  may  then  be  opened  and  sprung  upon  the 
neck,  to  which  it  will  cling,  and  along  which  it  may  be 
FIG.  135.  moved  to  any  desired  position. 


NATURE  AND  EFFECTS   OF  HEAT 


151 


containing  vessel,  the  method  described  in  the  following 
experiment  is  employed. 

It  depends  upon  the  fact  that  the  height  of  liquid 
columns  which  balance  one  another  are  inversely  as  their 
respective  densities,  and  dependent  only  upon  the  densities. 

In  this  experiment,  which  is  due  to  the  French  physicist 
Regnault,  two  connecting  ver- 
tical tubes  of  glass  (Fig.  136) 
are  filled  with  the  liquid  to  be 
tested.  One  of  these  is  packed 
with  ice,  while  the  other  is  sur- 
rounded with  steam.  The  dif- 
ference in  the  height  of  the 
two  columns  affords  a  measure 
of  the  relative  density  of  the 
liquid  within  the  two  arms,  Fl<>.  136. 

and  indirectly  of  the  expansion  which  the  former  under- 
goes when  heated. 

135.  Expansion  of  Gases.  —  The  mere  fact  of  the  expan- 
sion of  gases  may  be  demonstrated  by  means  of  apparatus 


FIG.  137. 

analogous  to  that  used  for  the  relative  expansion  of 
liquids;  i.e.  the  glass  bulb  6,  Fig.  137.  This  is  slightly 
heated,  and  the  bent  end  of  the  long  neck  is  plunged  into 
mercury.  Upon  cooling,  the  liquid  rises  into  the  neck, 
which  should  be  slightly  inclined  from  the  horizontal 
position,  as  shown  in  the  figure. 

The  gas,  when  even  slightly  heated,  as  by  the  applica- 


152  THE   OUTLINES   OF  PHYSICS 

tion  of  the  band  to  the  bulb,  drives  the  mercury  outward 
along  the  neck;  and  when  the  gas  cools,  the  mercury 
returns  up  the  neck  towards  the  bulb.  Some  of  the 
earliest  thermometers,  devised  by  Galileo  and  by  Newton, 
were  based  upon  the  same  principle  as  this  simple  appa- 
ratus. 

136.  Thermometry.  —  In  order  to  make  use  of  the  expan- 
sion of  any  substance  for  the  measurement  of  temperature, 
it  is  necessary  to  select  at  least  two  fixed  temperatures  of 
reference  and  to  have  some  scale  by  means  of  which  to 
express  the  changes  which  occur.  Common  experience 
has  led  to  the  adoption  of  the  temperature  of  melting  ice, 
and  that  of  steam  rising  from  water  which  boils  under 
a  pressure  of  76  cm.,  for  the  constant  temperatures  of 
reference. 

Many  therrnometric  scales  have  been  devised,  but  the 
one  used  in  scientific  work  in  all  parts  of  the  world  is  the 
centigrade  scale  devised  by  Celsius. 

In  this  scale  the  temperature  of  melting  ice  is  desig- 
nated as  zero  (0°  C.),  and  the  interval  between  the  ice 
point  and  the  steam  point  is  divided  into  one  hundred 
equal  parts,  called  degrees.  The  designation  of  the  steam 
temperature  at  76  cm.  pressure  is  therefore  100°  C. 

As  the  result  of  common  experience,  likewise,  the  rela- 
tive expansion  of  mercury  in  glass  has  been  adopted  as 
the  most  convenient  and  trustworthy  means  of  indicating 
ordinary  changes  of  temperature.  The  instrument  most 
widely  used  in  thermometry  is  therefore  the  mercury  ther- 
mometer. It  is  constructed  as  follows  : 

A  tube  with  capillary  bore  is  sealed  at  one  end,  and  the 
sealed  end  is  blown  out  into  an  elongated  bulb.  The  bulb 
is  filled  with  mercury,  and  is  then  heated  to  a  temperature 


NATURE  AND   EFFECTS   OF  HEAT 


153 


above  the  highest  at  which  the  instrument  is  to  be  used. 
When  thus  heated  the  expanded  mercury  must  entirely 
fill  the  tube.  The  open  end  is  then  sealed  by  melting,  and 
sometimes  a  small  secondary  bulb  (v)  is  blown. 

Figure    138   shows    the    typical   form  of   the    mercury 
thermometer  as  constructed  for  scientific  measurements. 

137.    Graduation   of   a   Thermometer.  —  When   the   ther- 
mometer, constructed  as  described  in  the  preceding  para- 

(o) 


-100 


FIG.  138. 


FIG.  139. 


FIG.  140. 


graph,  is  to  be  provided  with  a  scale,  it  is  placed  with  its 
bulb  closely  surrounded  with  melting  ice  (Fig.  139),  and 
the  point  within  the  bore  to  which  the  top  of  the  mercury 


154  THE  OUTLINES   OF  PHYSICS 

column  recedes  is  marked.     This  is  the  ice  point  i,  and  is 
taken  as  the  zero  of  the  scale. 

The  thermometer  is  then  placed  in  a  steam  bath  (Fig. 
140),  at  a  pressure  of  76  cm.,  and  the  height  reached  by 
the  mercury  is  noted.  This  is  the  steam  point  s,  and 
becomes  the  100°  point  of  the  scale.  It  now  remains  only 
to  divide  the  interval  between  i  and  s  into  one  hundred 
equal  parts.  Were  the  bore  of  the  thermometer  a  true 
cylinder,  these  would  be  divisions  of  equal  length.  Owing 
to  the  irregularities  of  the  tube,  they  must,  however,  be 
made  of  unequal  lengths,  but  in  such  a  manner  that  the 
successive  intervening  spaces  shall  contain  equal  volumes. 
The  process  by  means  of  which  the  proper  lengths  are 
determined  is  called  the  calibration  of  the  tube.  It  con- 
sists in  detaching  within  the  tube  a  thread  of  mercury 
(Fig.  141)  and  moving  it  stepwise  through  the  tube,  not- 
ing its  length  at  each  step.  The  reciprocals  of  the  various 


Ill    MM 


if  I  MI 


FIG. 141. 

lengths  thus  determined  afford  a  measure  of  the  varying 
cross-section. 

The  portions  of  the  tube  lying  below  the  ice  point  and 
above  the  steam  point  are  divided  into  parts  equal  to 
those  between  0°  and  100°.  The  former  are  distinguished 
by  the  negative  sign. 

138.  EXPERIMENT  36.  —  Calibration  of  the  Bore  of  a  Capillary 
Tube.  The  method  described  above  affords  the  means  of  an  interest- 
ing and  instructive  exercise,  which  for  the  sake  of  convenience  may 
be  made  with  a  piece  of  open  tubing  of  small  bore.  This  method  of 
calibration  is  of  especial  importance,  because  it  is  applicable  to  many 
instruments  besides  the  thermometer. 


NATURE  AND  EFFECTS   OF  HEAT  155 

Apparatus : 

(1)  A  piece  of  capillary  tubing,  about  30  cm.  long,  and  open  at 
both  ends ;  a  tube  of  bore  so  small  that  a  short  thread  of  mercury 
will  maintain  its  position  within,  with  the  tube  vertical,  but  moving 
freely  when  the  tube  is  tapped,  is  to  be  preferred. 

(2)  A  strip  of  cross-section  paper ;  some  mercury. 
Procedure : 

(a)  Introduce  into  the  tube  a  sufficient  amount  of  mercury  to 
make  a  thread  about  2  cm.  long.  This  is  brought  nearly  to  one  end 
by  tapping  the  tube. 

(6)  Lay  the  tube  horizontally  upon  the  cross-section  paper,  its  axis 
perpendicular  to  one  of  the  sets  of  lines,  and  determine  the  length  of 
the  thread  in  terms  of  the  number  of  spaces  (or  scale  divisions)  which 
it  covers,  also  the  distance  of  the  nearer  end  of  the  thread  from  the 
end  of  the  tube,  or  from  a  mark  thereon  which  has  been  placed  as  a 
zero  of  reference.  Move  the  thread  by  about  its  own  length,  towards 
the  middle  of  the  tube  and  repeat  the  measurements.  Continue  thus 
until  nearly  the  whole  length  of  the  tube  has  been  traversed. 

(c)  Tabulate  the  readings  as  below,  making  out  the  remainder  of 
the  table  by  computation. 

The  result  of  these  measurements  will  be  to  show  that  the  bore  is 
not  uniform.  Generally  speaking,  it  will  be  found  conical  in  form, 
but  with  more  or  less  marked  irregularities.  The  character  of  the 
bore  should  finally  be  indicated  by  plotting  a  curve  in  which  abscissas 
are  the  successive  distances  of  the  middle  of  the  thread  from  zero, 
i.e.  from  the  end  of  the  tube,  and  ordinates  are  the  reciprocals  *  of  the 
relative  lengths  of  thread.  For  a  truly  cylindrical  tube  this  curve 
would  be  a  horizontal  line,  the  distance  of  which  above  the  base  line 
is  proportional  to  the  cross-section  of  the  bore.  For  a  regularly  coni- 
cal tube,  the  line  would  be  oblique.  In  the  case  of  most  actual  tubes 
the  curve  takes  a  form  of  which  that  in  Fig.  142  is  typical. 

139.  Mercury  in  Glass  Temperatures.  —  The  desirability 
of  the  thermometric  scale  just  described,  regarded  as  a 

1  Reciprocals  are  plotted  instead  of  lengths,  because  the  latter  are  in- 
versely as  the  cross-section,  or  as  the  volume  per  unit  length  of  tube, 
whereas  the  reciprocals  are  directly  proportional  to  the  volumes.  The 
curve  therefore  gives  a  sort  of  picture,  very  much  exaggerated,  of  the 
irregularities  of  the  bore. 


156 


THE   OUTLINES   OF  PHYSICS 


TABLE. 
CALIBRATION  OF  A  CAPILLARY  TUBE. 


No. 

READINGS. 

Length  of  thread  in 
scale  divisions  (f). 

Position  of  middle 
of  thread  (=  dis- 
tance of  a  from 
zero  +  3^)- 

Kc'lative  lengths  in 
terms  of  mean 
length 

L  i  \ 

V  1-022T' 

"aS         ^_^ 

»=  fU 

it  - 

2g-*^ 

•S  o  g 

£•-3 

End  a  (dis- 
tance in  scale 
divisions  from 
zero). 

End  &  (dis- 
tance in  scale 
divisions  from 
zero). 

1 

0-00 

1-04 

1-04 

0.520 

1-017 

0-983 

2 

1-19 

2-23 

1-04 

1-710 

1-017 

0-983 

3 

1-98 

3-01 

1-03 

2-495 

1-007 

0-993 

4 

3-04 

4-06 

1-02 

3-550 

0-997 

1-003 

5 

4-00 

5-03 

1-03 

4-515 

1-007 

0-993 

6 

4-88 

5-90 

1-02 

5-390 

0-997 

1-003 

7 

6-01 

7-03 

1-02 

6-520 

0-997 

1-003 

8 

7-12 

8-17 

1-05 

7-745 

1-027 

0-972 

9 

8-21 

9-23 

1-02 

8-720 

0-997 

1-003 

10 

9-20 

10-22 

1-02 

9-710 

0-997 

1-003 

11 

10-20 

11-23 

1-03 

10-715 

1-007 

0-993 

12 

11*16 

12-17 

1-02 

11-660 

0-997 

1-003 

13 

12-13 

13-14 

1-01 

12-635 

0-988 

1-013 

14 

13-19 

14-20 

1-01 

13-695 

0-988 

1-013 

15 

14-17 

15-19 

1-02 

14-680 

0-997 

1-003 

16 

15-07 

16-09 

1-02 

15-580 

0-997 

1-003 

17 

16-12 

17-14 

1-02 

16-630 

0-997 

1-003 

18 

17-22 

18-24 

1-02 

17-730 

0-997 

1-003 

19 

18-31 

19-32 

1-01 

18-815 

0-988 

1-013 

20 

19-81 

20-83 

1-02 

20-320 

0-997 

1-003 

21 

20-95 

21-98 

1-03 

21-465 

1-007 

0-993 

22 

21-97 

22-99 

1-02 

22-470 

0-997 

1-003 

23 

22-99 

24-00 

1-01 

23-495 

0-988 

1-013 

24 

24-07 

25-08 

1-01 

24.575 

0-988 

1-013 

Mean  length  =  1-0227. 


NATURE  AND   EFFECTS   OF  HEAT 


157 


device  for  measuring  temperature,  depends  upon  the  accu- 
racy with  which  its  successive  intervals  correspond  to 
equal  accessions  of  temperature.  They  would  correspond 
precisely,  provided  the  relative  expansion  of  mercury  were 
uniform.  That  liquid,  however,  expands  more  rapidly  at 
high  than  at  low  temperatures,  and  the  same  thing  is 


FIG.  142. 

true  to  a  much  greater  extent  of  the  glass  bulb.  Between 
0°  and  100°  the  errors  due  to  this  cause  are  slight,  amount- 
ing to  only  a  fraction  of  one  degree.  In  scientific  work 
of  such  accuracy  that  these  small  errors  are  of  importance, 
it  is  customary  to  indicate  the  nature  of  the  scale  by 
designating  the  temperatures  as  mercury  in  glass  tempera- 
tures. 

140.  Charles's  Law;  the  Air  Thermometer.  —  All  solids 
and  liquids  show  variations  in  the  law  of  their  expansion. 
Perfect  gases,  however,  expand  uniformly,  obeying  the 
following  laws : 

(1)  When  various  gases  are  equally  heated  under  con- 
stant pressure,  they  all  suffer  the  same  expansion. 


158 


THE  OUTLINES   OF  PHYSICS 


(2)  For  every  degree  centigrade  ivhich  a  gas  is  heated,  it 
expands  by  an  amount  equal  to  ^-|-g-  of  its  volume  at  0°  C. 

This  law  is  known  as  Charles's  Law  and  also  as  Gay 
Lussac's  Law.  It  was  enunciated  by  the  former  physicist 
in  1787,  and  more  completely  developed  by  the  latter  in 
1802. 

On  account  of  this  uniformity,  the  expansion  of  gases 
has  been  made  the  basis  of  the  standard  scale  of  tempera- 
tures, to  which  all  other  scales  are  referred  for  comparison 
or  correction.  The  two  standard  temperatures  of  refer- 
ence, as  in  the  case  of  the  mercury  thermometer,  are  the 
ice  and  steam  point  (see  Art.  137),  and  the  interval  is 
divided  into  one  hundred  degrees.  When 
the  ice  point  is  taken  as  zero,  the  scale  is 
called  the  centigrade  scale  of  the  air  ther- 
mometer. 

It  is  sometimes  more  convenient  to  use 
as  the  zero  of  the  scale  a  hypothetical  point 
called  the  absolute  zero.  This  may  be  de- 
fined as  follows.  Imagine  an  air  ther- 
mometer cylindrical  in  form  (Fig.  143). 

Let  the  volume  of  a  contained  gas,  which 
we  must  suppose  separated  from  the  outer 
atmosphere  by  a  movable  film  which  it 
drives  before  it  when  heated,  occupy  the 
tube  up  to  the  line  marked  ice,  when 
brought  to  the  temperature  of  melting  ice, 
and  let  it  expand  to  the  line  marked  steam, 
when  heated  to  the  temperature  of  the 
vapor  of  water  which  boils  at  76  cm. 

FIG.  143. 

pressure. 

If  we  mark  the  ice  point  0°  and  the  steam  point  100°, 
the  scale  will  be  the  centigrade  scale.  If  we  continue  to 


NATURE  AND  EFFECTS   OF  HEAT 


159 


divide  the  tube,  using  degrees  equal  to  T^,  the  distance 
between  the  ice  point  and  steam  point,  the  bottom  of  the 
tube  will  coincide  with  scale  division  —273°  C.  If  we 
adopt  this  mark  as  the  zero  of  our  scale  and  divide  the 
entire  tube  into  degrees  of  the  same  size  as  before,  the 
ice  point  becomes  -h  273°  and 
the  steam  point  +  373°.  The 
zero  thus  chosen  is  called  the 
absolute  zero,  and  the  scale  is 
called  the  absolute  scale  of  the 
air  thermometer. 

141.  The  Air  Thermometer. 
—  It  is  not  practicable  to  give 
the  air  thermometer  the  sim- 
ple form  suggested  in  the 
previous  paragraph.  The  es- 
sential features  of  the  actual 
instrument  are  shown  in  Fig. 
144.  These  are  a  bulb  of 
glass  or  porcelain  (^L),  which 
contains  the  dry  gas  (usually 
air  or  hydrogen),  the  ten- 
dency of  which  to  expand  is 
to  be  utilized.  The  neck  of 
this  bulb  is  very  narrow,  and  it  ends  in  one  arm  of  the 
manometer  mv  w2.  The  other  arm  (w2)  is  long,  and  is 
closed  at  its  upper  end.  The  space  (y)  above  the  mer- 
cury in  this  arm  contains  no  air,  so  that  the  manometer 
may  be  considered  as  a  siphon  barometer  in  which  the 
vertical  distance  A,  between  a  and  5,  measured  in  centi- 
meters, gives  the  pressure  exerted  upon  the  gas  in  A. 

When  the  gas  is  heated  it  expands,  driving  the  mercury 


FIG.  144. 


160  THE  OUTLINES   OF  PHYSICS 

downwards  at  a  and  upwards  at  b.  This  movement  is 
counterbalanced  by  raising  the  cistern  (7  until  the  level 
at  a  is  restored.  The  pressure,  as  indicated  by  the  differ- 
ence of  level  A,  necessary  to  maintain  the  mercury  at  the 
fixed  point  «,  when  the  temperature  of  the  gas  is  £°,  as 
compared  with  that  necessary  to  give  the  gas  the  same 
volume  at  the  temperature  £0°,  measures  the  change  of 
temperature,  t  —  tQ. 

This  is  called  the  method  of  constant  volumes. 

The  advantage  of  the  air  thermometer  over  other  de- 
vices for  the  measurement  of  temperature,  is  that  it  ful- 
fills more  nearly  the  conditions  necessary  to  an  absolute 
standard  or  system.  Mercury  thermometers  are  so  much 
more  convenient,  however,  that  they  are  almost  always 
used,  and  the  air  thermometer  is  reserved  for  the  study  of 
the  errors  of  reading  of  such  instruments. 


CALOEIMETRT  161 


CHAPTER  XVII 

CALORIMETRY 

142.  Heat  a  Form  of  Energy.  —  When  the  temperature  of 
a  body  rises,  energy  of  the  form  which   we    call    heat    is 
stored  very  much  as  potential  energy  is  stored  in  bodies 
which  are  elevated  against  the  force  of  gravity  to  some 
higher  position.     Rise  of  temperature  is,  therefore,  always 
an  indication  that  work  is  being  done.     A  body,  in  other 
words,  cannot  be  heated  without  the  expenditure  of  energy. 
When  it  cools,  the  energy  stored  in  it  is  given  up  again, 
either  in  the  way  of  raising  the  temperature,  and  thus 
increasing  the  stock  of  stored  energy  in  neighboring  bodies, 
or  in  producing  motion. 

Since  heat  is  a  form  of  energy,  it  follows  that  it  is 
capable  of  being  measured.  The  art  of  thus  measuring 
quantities  of  heat,  as  distinguished  from  the  mere  measure- 
ment of  temperature,  is  called  Calorimetry. 

143.  Capacity  for  Heat.  —  The  amount  of  work  which  it 
is  necessary  to  do  to  raise  different  substances  in  tempera- 
ture varies  with  the  nature  of  the  material.     The  amount 
of  heat  required  to  raise  any  given  body  1°  C.  in  tempera- 
ture measures  its   capacity  for  heat  (thermal  capacity). 
In  order  to  compare  the  thermal  capacities  of  different 
substances,  water  is  selected  as  a  standard.     Water  is  a 
convenient  substance  for  this  purpose  for  many  reasons, 
the  most  important  of  which  is  that  its  capacity  for  heat 
is  very  nearly  uniform  through  whatever  range  of  tem- 


162  THE  OUTLINES   OF  PHYSICS 

perature  it  may  be  carried.  The  uniformity  of  the  thermal 
capacity  of  water  may  be  demonstrated  by  means  of  the 
following  experiment. 

144.  EXPERIMENT  37.  —  The  Uniformity  of  the  Thermal  Capacity 
of  Water. 

Apparatus : 

(1)  Three  beakers,  two  of  which  are  of  the  same  size  (about  400 
cc.),  the  other  rather  more  than  twice  as  large. 

(2)  Two  flasks. 

(3)  Two  thermometers. 

(4)  Some  crushed  ice. 

(5)  A  Bunsen  burner. 

(6)  A  balance  and  weights. 
Procedure : 

(a)  Note  the  temperature  of  the  room,  as  indicated  by  one  of  the 
thermometers,  and  select  two  temperatures,  one  as  many  degrees 
above  the  room  temperature  as  the  other  is  below  it  (for  example,  if 
the  temperature  of  the  room  be  20°  C.,  5°  C.  may  be  selected  as  the 
lower,  and  35°  C.  as  the  higher  temperature). 

(&)  Place  the  small  beakers  upon  the  pans  of  the  balance  and  add 
shot  or  small  weights  to  the  lighter  pan  until  equilibrium  is  produced. 

(c)  Cool  a  flaskful  of  water  to  the  lower  temperature  selected 
(say  5°)  by  adding  bits  of  ice  and  stirring.  At  the  same  time  warm 
the  other  flaskful  of  water  to  the  higher  temperature  (say  35°). 

((/)  Nearly  fill  one  of  the  beakers  upon  the  balance  with  the  warm 
water,  then  pour  cold  water  enough  into  the  other  beaker  to  exactly 
counterbalance  it. 

(e)  Remove  the  beakers  simultaneously  from  the  balance,  insert 
the  thermometers,  one  in  each  beaker,  stir,  and  read  the  temperatures. 
Transfer  both  thermometers  to  the  large  beaker,  and,  without  delay, 
pour  the  cold  and  warm  water  simultaneously  into  the  same.  Stir 
the  mixed  contents,  using  both  thermometers  as  stirrers,  until  the 
temperature  comes  into  equilibrium.  Read  the  temperature,  using 
both  thermometers. 

(/)  Subtract  the  final  temperature  as  indicated  upon  the  ther- 
mometer previously  used  for  determining  the  temperature  of  the  cold 
water  from  the  temperature  which  that  water  had  before  mixing,  and 


CALORIMETB  Y  163 

subtract  from  the  temperature  of  the  hot  water  the  final  temperature 
of  the  mixture  as  indicated  by  the  second  thermometer. 

Since  the  thermal  capacity  of  water  is  constant,  and  since  the  cold 
water  is  heated  by  the  expenditure  of  energy  derived  from  the  cooling 
of  the  warm  water,  the  final  temperature  should  be  midway  between 
the  initial  temperatures.  The  fact,  on  the  other  hand,  that  when  this 
experiment  is  properly  performed  the  final  temperature  is  thus  related 
to  the  initial  temperatures  demonstrates  the  constancy  of  the  thermal 
capacity  of  water. 

145.  Specific  Heat.  —  The  thermal  capacity  of  a  body, 
as  compared  with  that  of  water,  or,  in  other  words,  the 
amount   of   heat   necessary  to  raise  a  gram  of  any  sub- 
stance 1°  C.,  as  compared  with  the  amount  of  heat  neces- 
sary to  raise  1  gram  of  water  from  0°  C.  to  1°  C.,  is  called 
the  specific  heat  of  the  substance. 

146.  Heat  Units.  —  The   quantity  of  heat  necessary  to 
raise  1  gram  of  water  1°  C.  is  termed  a  heat  unit.     The 
name  given  to    this  unit  is  the  calorie.     A  larger  heat 
unit   is    sometimes    desirable,    as,   for   example,    in   cases 
where  the  expenditure  of  large  quantities  of  heat  energy 
is  to  be  considered.     The  larger  unit  generally  selected 
is   the   amount  of  heat  necessary  to  raise  1  kilogram  of 
water  1°  C.     This  is  equal  to  1000  calories. 

147.  Methods  of  determining  Specific  Heat.  —  The  Method 
of  Mixtures.      The  simplest  and  most  direct   method  of 
measuring  specific  heat  consists  in  ascertaining  how  great 
a  rise  of  temperature  the  body  under  investigation  is  capa- 
ble of   imparting  to  a  known  mass  of  water,  when  the 
former  is  cooled  through  a  known  range  of  temperature. 
This  method  may  be  best  illustrated  by  means  of  the  fol- 
lowing experiment : 


164 


THE  OUTLINES   OF  PHYSICS 


148.   EXPERIMENT  38.  —  Specific  Heat  of  a  Metal. 

Apparatus  : 

(1)  A  cylindrical  vessel  of  sheet  copper  about  10  cm.  high  and 
10  cm.  in  diameter.     (This  vessel,  which  constitutes  the  calorimeter, 
that  is  to  say,  the  apparatus  for  the  measurement  of  heat  quantities, 
should  be  polished,  in  order  to  reduce  so  far  as  possible  its  radiating 
power.) 

(2)  A  piece  of  lead,  brass,  or  copper,  preferably  spherical  or  cylin- 
drical in  form,  the  mass  of  which  is  about  500  grams. 

(3)  Two  thermometers,  one  of  which  should  be  accurate  and  sensi- 
tive. 

(4)  A  balance  and  weights,  a  Bunsen  burner,  and  a  small  quantity 
of  crushed  ice. 

Procedure  : 

(a)  Weigh  the  calorimeter  and  the  metal  body,  the  specific  heat  of 
which  is  to  be  determined.  To  the  latter  a  strong  bit  of  twine  about 
50  cm.  long,  or  a  fine  wire,  should  have  been  attached,  and  the  same 
should  be  weighed  along  with  the  mass  of  metal. 

(6)  Place  the  weight  in  a  beaker  or 
can  of  water  over  the  Bunsen  flame  ; 
bring  the  liquid  to  boiling,  and  allow 
it  to  remain  at  that  temperature  for 
several  minutes.  In  the  meantime 
place  the  calorimeter  upon  the  scale 
pan  of  the  balance,  half  fill  it  with 
water,  and  weigh  again. 

(c)  Remove  the  calorimeter  to  the 
laboratory  table,  and  mount  it  upon 
wooden  wedge-shaped  blocks  at  the 
foot  of  a  support,  as  shown  in  Fig. 
145.  Determine  carefully  the  tem- 
perature of  the  water  which  it  con- 
tains; also,  by  means  of  the  other 
thermometer,  determine  the  tempera- 


'  . 


rounds  the  metal  weight. 

(c?)  Remove  the  weight  from  the 
boiling  water  by  means  of  the  twine  or  wire,  the  free  end  of  which 
should  have  remained  outside  the  vessel  for  this  purpose,  and  trans- 


CALORIMETRY  165 

fer  it  as  promptly  a.3  possible  to  the  calorimeter.  It  may  be  sus- 
pended from  an  arm  of  the  support,  as  shown  in  the  figure.  Then, 
by  means  of  the  thermometer,  which  should  have  remained  im- 
mersed in  the  liquid  of  the  calorimeter,  stir  the  contents  of  that 
vessel,  continuing  to  do  so  as  long  as  the  temperature  rises.  Note 
carefully  the  highest  temperature  which  the  thermometer  reaches. 

(e)  From  the  rise  of  temperature  which  the  water  has  undergone, 
its  mass,  the  fall  of  temperature  suffered  by  the  hot  body  after  its 
introduction  into  the  calorimeter,  and  its  mass,  the  specific  heat  of  the 
latter  may  be  computed.  This  quantity,  which  we  may  call  Q,  will 
be  expressed  by  means  of  the  following  equation, 

0_W(t"  -t'} 
'  ' 


in  which  W  is  the  weight  of  the  water  in  grams,  S  the  weight  of  the 
metal,  t  the  original  temperature  of  the  metal,  t'  that  of  the  water, 
and  t"  the  final  temperature  which  they  reach  in  common,  after  having 
been  brought  together  within  the  calorimeter. 

A  small  part  of  the  heat  energy,  derived  from  the  cooling  of  the 
metal,  goes  to  warming  the  walls  of  the  calorimeter.  This  quantity, 
which  has  been  neglected  in  the  computation  indicated  above,  may  be 
found  by  multiplying  the  mass  of  the  calorimeter  by  the  specific  heat 
of  copper  (0-093)  and  by  the  rise  of  temperature  which  it  underwent 
during  the  experiment.  In  all  exact  determinations  of  specific  heat 
this  correction  is  made. 


149.  Specific  Heats  of  Solids,  Liquids,  and  Gases.  —  In  the 

table  on  the  following  page  are  given  the  specific  heats  of 
various  substances. 

150.  Method  of  the  Ice-Block  Calorimeter.  —  As  will  be 
shown  in  a  subsequent  article  (see  Art.  153),  a  perfectly 
definite  amount  of  heat  is  required  to  melt  a  gram  of  ice 
and  convert  the  same  into  the  liquid  state.     Advantage  is 
sometimes  taken  of  this  fact  for  the  determination  of  spe- 
cific heats.     Indeed,  this,  which  was   one  of  the  earliest 


166 


THE  OUTLINES   OF  PHYSICS 


TABLE. 
(1)    SPECIFIC  HEATS  OF  SOME  OF  THE  COMMON  ELEMENTS. 


Substances. 

Temps. 

Sp.  Heat. 

Substances. 

Temps. 

Sp.  Heat. 

Aluminium  .     .     . 

0°-100° 

0-2185 

Manganese  . 

14°-  97° 

0-1217 

Antimony    .     .     . 

0°-100° 

0-4950 

Mercury  .     . 

20°-  50° 

0-0331 

Bismuth  .... 

20°-  84° 

0-3050 

Nickel     .     . 

14°-  97° 

0-1091 

Cadmium     .     .     . 

0°-100° 

0-1804 

Phosphorus  : 

Carbon  (diamond) 

0°-100° 

0-1450 

(Red).     . 

15°-  98° 

01698 

"        (graphite) 

0°-100° 

0-1860 

(Yellow)  . 

13°-  36° 

0-2020 

Copper    .... 

0°-100° 

0-0933 

Platinum     . 

0°-100° 

0-0323 

Gold    

0°-100° 

0-0316 

Silver.     .     . 

0°-100° 

0-0568 

Iron    

0°-100° 

0-1130 

Sulphur  .     . 

15°-  97° 

0-1844 

Lead   

0°-100° 

0-0315 

Tin      ... 

0°-100° 

0-0559 

Magnesium  .     .     . 

20°-51° 

0-245 

Zinc    .     .     . 

0°-100° 

0-0938 

(2)    SPECIFIC  HEATS  OF  COMPOUNDS. 


Substances. 

Temps. 

Sp.  Heat. 

Substances. 

Temps. 

Sp.  Heat. 

Bell  metal    .     .     . 

15°-  98° 

0-0850 

Glass  : 

Brass  

0° 

0-0890 

(  Plate") 

10°-  50° 

0-186 

Bronze     .... 

20°-100° 

0-1043 

(Crown)  . 

10°-  50° 

0161 

(88-7  Cu+1  1-3  Al) 

(Flint)     . 

10°-  50° 

0117 

German  silver.     . 

0°-100° 

0-0946 





Paraffin  .     . 

10°-  15° 

0-562 

Quartz     .... 

20°-  50° 

0-1860 

Wax   .     .     . 

26°-  42° 

0-820 

Granite    .... 

12°-100° 

0-1900 

Vulcanite    . 

20°-100° 

0-331 

Marble     .... 

18°-  99° 

0-2080 

Ice.     .     .     . 

-  30°    -0° 

0-505 

CALORIMETEY  167 


methods,  was  described  by  Black,  an  English  physicist,  in 
1772.  The  form  of  the  experiment  is  as  follows: 

151.  EXPERIMENT  39.— Specific  Heat  by  the  Method  of  the  Ice- 
Block  Calorimeter. 

Apparatus : 

(1)  A  block  of  clear  ice  20  x  20  x  20  cm.;    also  a  slab  of  ice 
20  x  20  cm.,  and  about  5  cm.  in  thickness.     In.  the  upper  surface  of 
the  block  a  cavity  is  made.     The  walls  of 

this  cavity  should  be  as  smooth  as  possible. 
The  most  convenient  method  for  producing 
such  a  hole  consists  in  cutting  it  out  in  the 
rough  with  a  knife,  and  then  finishing  it 
by  inserting  a  cylindrical  weight  of  metal 
previously  heated,  or  a  small  bottle  con- 
taining hot  water.  After  a  cavity  has  been 
made,  the  size  of  which  is  sufficient  to  re-  FlG 

ceive  the  mass  of  metal  the  specific  heat  of 

which  is  to  be  determined,  the  interior  is  dried  by  wiping  with  filter 
paper,  and  the  slab  of  ice  is  replaced.  The  ice-block  calorimeter 
thus  formed  will  appear  as  in  Fig.  146. 

(2)  A  balance  and  weights. 

(3)  The  piece  of  metal  used  in  Experiment  38 ;  also  a  beaker  of 
boiling  water,  two  thermometers,  and  a  sponge.1 

Procedure  : 

(a)  The  mass  of  the  metal  is  determined  by  weighing,  and  it  is 
heated  as  in  the  previous  determination. 

(t>)  Having  been  subjected  to  the  action  of  boiling  water  for  a  suffi- 
cient time,  namely,  several  minutes,  the  weight  is  removed  by  means 
of  the  attached  twine,  and*  is  placed  in  the  cavity  of  the  ice  block 
which  just  previously  must  have  been  newly  dried  with  the  filter 
paper.  The  slab  is  instantly  replaced,  and  a  sufficient  amount  of  time 
is  allowed  to  elapse  to  cool  the  hot  metal  to  the  ice  temperature. 
Not  less  than  ten  minutes  should  be  allowed  for  this  portion  of  the 
experiment;  and  if  large  masses  of  metal  are  dealt  with,  a  longer 
amount  of  time  is  required. 

(c)  The  slab  is  removed,  and  the  weight  is  carefully  withdrawn 

1  Instead  of  the  sponge,  several  sheets  of  filter  paper  may  be  used. 


168  THE  OUTLINES   OF  PHYSICS 

from  the  ice  cavity,  and  is  dried  by  contact  with  the  sponge,  or  with 
a  wad  of  filter  paper  which  has  been  previously  weighed.  The  same 
sponge  or  filter  paper  is  then  employed  in  removing  from  the  cavity  of 
the  ice  block  all  the  liquid  which  has  resulted  from  the  melting  of  the 
ice  therein.  The  paper,  with  the  water  which  has  been  taken  up,  is 
placed  in  the  beaker,  the  weight  of  which  had  also  been  previously 
determined,  and  is  weighed  again.  In  this  way  the  amount  of  ice 
melted  is  determined.  The  success  of  the  experiment  depends  upon 
fashioning  the  ice  block  in  such  a  way  that  none  of  the  liquid  formed 
by  the  exterior  melting  will  fall  into  the  cavity.  This  end  may  be 
secured  by  slightly  beveling  off  the  upper  face  of  the  block  so  that 
the  drainage  from  that  face  will  be  outward,  and  by  giving  the  under 
face  of  the  slab  which  is  used  as  a  cover  a  slight  degree  of  concavity. 

(rf)  The  computation  of  the  result  of  this  experiment  is  as  follows : 
The  amount  of  heat  energy  required  to  melt  1  gram  of  ice  is  accu- 
rately known ;  it  is  79-25  calories.  (See  Art.  153.)  The  mass  of  the 
hot  metal  being  known,  and  the  fall  of  temperature  which  it  suffered, 
namely,  from  the  boiling  point  of  water  to  the  melting  point,  we  may 
compute  the  number  of  calories  which  one  gram  of  similar  material 
would  have  given  up  in  cooling  1°  C.  This  is  obviously  the  number 
of  calories  required  to  melt  the  ice,  divided  by  the  product  of  the  mass 
of  metal  into  the  fall  of  temperature.  The  number  of  calories  which 
a  gram  of  the  material  would  give  up  in  a  fall  of  1°  C.  measures, 
however,  the  specific  heat  of  the  material. 

The  formula  by  means  of  which  these  statements  are  to  be  ex- 
pressed, and  which  serves,  therefore,  for  the  computation  of  the 
specific  heat,  is  n  _  79-25  TF 

~~slT' 

where  W  is  the  mass  of  ice  melted, 

S  is  the  mass  of  the  metal,  * 
t  is  the  temperature  of  the  hot  bath. 

152.  Specific  Heat  of  Gases  and  Liquids.  —  The  specific 
heats  of  gases  and  liquids  are  determined  by  methods 
based  upon  the  principles  just  described.  Many  modifica- 
tions in  the  procedure  are  necessary,  however,  and  it  will 
not  be  possible  to  describe  these  in  detail  in  the  present 
work. 


CALOEIMETEY  169 

153.  Heat  of  Fusion.  —  The  amount  of  heat  necessary  to 
melt  a  unit  mass  of  any  substance,  converting  it  into  liquid 
form  without  rise  of   temperature,  is  called  the  heat  of 
fusion.     This  is  a  perfectly  definite  quantity,  always  pos- 
sessing the  same  value  in  the  case  of  a  given  liquid,  but 
differing  much  with  different  substances. 

Heat  of  fusion  of  water  is  much  larger  than  that  of 
other  liquids.  It  amounts  to  nearly  eighty  calories  (79-25 
calories).  To  convert  ice  at  0°  C.  into  water  at  0°  C.,  in 
other  words,  requires  as  much  heat  as  to  raise  water  at  0°  C. 
to  80°  C.  If  we  take  500  grams  of  water  at  80°  C.,  for 
example,  and  place  in  it  the  same  amount  of  ice,  the  heat 
liberated  by  the  water  on  cooling  will  be  just  sufficient  to 
melt  all  the  ice.  The  final  temperature,  instead  of  being 
midway  between  the  two  initial  temperatures  (Art.  144), 
will  be  0°  C.  The  experiment  is  a  somewhat  difficult  one 
to  carry  out  in  this  especial  form,  owing  to  the  loss  of  heat 
to  surrounding  objects.  The  following  is  a  better  method: 

154.  EXPERIMENT  40.  — Heat  of  Fusion  of  Water. 

Apparatus : 

(1)  The  ice-block  calorimeter  described  in  Experiment  39. 

(2)  A  balance  and  weights,  thermometer,  Bunsen  burner,  beakers, 
sponge,  etc. 

Procedure  : 

(a)  A  clean,  dry  beaker  is  placed  upon  the  scale  pan  and  weighed. 
A  quantity  of  water  is  then  added,  sufficient  to  half  fill  the  cavity  of 
the  ice  block,  and  its  weight  is  determined. 

(&)  The  beaker  of  water  is  removed  from  the  balance  and  heated 
to  80°  C.,  care  being  taken  during  this  operation  that  the  beaker  is 
covered  with  a  plate  of  glass  to  reduce  losses  by  evaporation  to  as 
small  a  quantity  as  possible.  When  the  water  has  reached  exactly 
80°  C.,  as  indicated  by  the  thermometer  used  as  a  stirrer  within  the 
liquid,  the  slab  is  removed  from  the  ice-block  calorimeter,  and  the 


170  THE  OUTLINES   OF  PHYSICS 

water  is  poured  without  delay  into  the  cavity.  The  latter  must  have 
been  previously  dried  by  the  application  of  filter  paper.  The  slab  is 
at  once  replaced,  and  a  sufficient  amount  of  time  is  given,  namely 
fifteen  minutes,  for  the  hot  water  to  have  delivered  all  its  heat  energy 
to  the  surrounding  ice.  It  is  obvious  that  when  this  condition  has 
been  reached,  the  temperature  of  the  water  within  the  cavity  will  have 
fallen  to  0°  C. ;  also  that  since  its  initial  temperature  was  80°  C.,  that 
the  amount  of  ice  that  it  should  be  capable  of  melting  is  equal  to  its 
own  mass.  It  is  the  object  of  the  experiment  to  verify  this  latter 
point. 

(c)  After  the  lapse  of  the  requisite  time,  remove  the  slab  from  the 
ice-block  calorimeter.  Withdraw  the  water  from  the  cavity  by  the 
use  of  a  sponge  to  the  beaker  previously  weighted,  care  being  taken 
to  lose  none.  Weigh  the  water  thus  accumulated,  and  compare  its 
mass  with  that  of  the  hot  water  applied  to  the  melting  of  the  ice. 
Two  small  corrections  are  necessary. 

(1)  That  due  to  the  fact  that  a  minute  quantity  of  water  clings  to 
the  beaker,  and  cannot  be  transmitted  to  the  ice  cavity.     This  amount 
may  be  quite  closely  estimated  by  weighing  the  beaker  filled  with 
water  as  described  under  section  (a),  pouring  it  out  as  nearly  as  possi- 
ble in  the  same  manner  as  when  the  hot  water  was  transmitted  to  the 
ice  cavity,  and  weighing  the  beaker  again.     The  increase  of  weight 
will  indicate  the  amount  of  this  correction. 

(2)  This  correction  arises  from  the  fact  of  the  loss  by  evaporation 
during  the  process  of   heating  the  liquid.     To  determine   this   the 
beaker  of  water  is  weighed ;  it  is  then  heated  as  nearly  as  possible 
under  the  same  conditions   as  in  the  actual  experiment  already  de- 
scribed, and  is  then  allowed  to  cool.     It  is  afterwards  weighed  again. 
Its  loss  of  weight  will  equal  (nearly)  twice  the   correction    due   to 
evaporation.     The  student  should  perform  these  operations,  and  thus 
determine  whether  these  corrections  are  of   sufficient  magnitude  to 
affect  his  result.     It  is  interesting  to  compare  the  heat  of  fusion  of 
ice  with  that  of  other  substances,  and  to  note  that  the  heat  of  vapori- 
zation of  water,  given  on  p.  178,  is  likewise  greatly  in  excess  of  that 
of  other  substances. 

155.  Numerical  Values  of  the  Heats  of  Fusion.  —  The 
heat  of  fusion  of  various  liquids  is  given  in  the  following 
table : 


CALORIMETEY 


171 


TABLE. 
HEAT  OF  FUSION  OF  VARIOUS  SUBSTANCES. 


Bismuth 

12-640  calories 

Mercury 

2-820 

Bromine 

16-185 

Paraffin 

35-100 

Cadmium 

13-660 

Phosphorus 

4-744 

Glycerine 

52-500 

Platinum 

27-180 

Ice 

79250 

Silver 

21-070 

Iron 

33-50 

Sulphur 

9-365 

Lead 

5-858 

Tin 

13-314 

156.  Heat  of  Vaporization.  —  When  liquids  are  converted 
into  the  state  of  vapor,  either  by  boiling  or  by  quiet  evapo- 
ration, a  certain  definite  amount  of  work  has  to  be  done 
upon  them.  Energy  is  stored  in  the  process  of  bringing 
about  this  change  of  state,  analogous  to  that  which  is 
stored  when  a  body  is  caused  to  rise  in  temperature. 
When,  on  the  other  hand,  a  vapor  is  condensed,  the  stored 
energy  becomes  available  again  and  may  be  made  to  do 
work  either  in  raising  the  temperature  of  other  bodies  or 
by  the  application  of  proper  devices,  as  in  the  steam  en- 
gine, in  the  production  of  motion.  The  heat  required  to 
vaporize  a  liquid  is,  generally  speaking,  a  very  large 
amount.  Water,  for  example,  when  converted  into  steam 
at  its  ordinary  boiling  point  (100°  C.)  requires  535  heat 
units  for  vaporization.  The  exact  measurement  of  the 
heat  of  vaporization  of  water  is  an  operation  of  consider- 
able difficulty,  but  the  phenomenon  may  be  illustrated  and 
the  numerical  value  of  the  heat  of  vaporization  may  be 
approximately  determined  by  means  of  the  following  very 
simple  experiment.  With  proper  care,  indeed,  excellent 
results  may  be  obtained. 


172 


THE   OUTLINES   OF  PHYSICS 


157.    EXPERIMENT  41.  —  The  Heat  of  Vaporization  of  Water. 

Apparatus  : 

(1)  A  flask  containing  about    1000  cm.3  of  water,  a  cork  which 
fits  it  well,  a  piece  of  glass  tube  about  GO  cm.  long  and  about  1  cm.  in 
external  diameter. 

(2)  A  balance  and  weights,  a  thermometer,  and  a  beaker. 

(3)  Two  Bunsen  burners. 

(4)  Crushed  ice. 
Procedure  : 

(a)  The  glass  tube  is  twice  bent  through  an  angle  of  90°,  giving 
it  the  form  shown  in  Fig.  147.     Its  shorter  arm  is  then  fitted  to  a 


FIG.  147. 


cork  which  is  inserted  in  the  mouth  of  the  flask.  Water  is  brought 
to  the  boiling  point  by  means  of  one  of  the  Bunsen  burners. 

(&)  The  beaker  is  filled  two  thirds  with  cold  water  chilled  as  near 
as  convenient  to  0°  by  the  use  of  ice.  The  mass  of  this  water  is 
determined  by  weighing. 

(c)  By  means  of  the  second  Bunsen  burner  the  horizontal  portion 
of  the  glass  tube,  through  which  the  steam  from  the  boiling  liquid 
is  being  delivered,  is  now  to  be  cautiously  heated  until  the  dropping 
of  condensed  vapor  from  its  open  end  ceases.  As  soon  as  this  condi- 
tion is  brought  about,  the  temperature  of  the  cold  water  within  the 
beaker  is  to  be  read  and  the  beaker  is  to  be  inserted  under  the  open 


CALORIMETRY 


173 


mouth  of  the  delivery  tube  so  that  the  latter  will  extend  to  a  depth 
of  three  or  four  centimeters  below  the  surface  of  the  liquid.  During 
the  remainder  of  the  experiment  the  beaker  must  be  supported  in  this 
position  by  means  of  blocks  placed  beneath  it.  Under  these  condi- 
tions, the  dry  steam  issuing  from  the  tube  will  be  entirely  condensed 
within  the  liquid  and  will  give  up  heat  energy  in  proportion  to  its 
mass  and  to  the  heat  of  vaporization,  thus  raising  the  temperature 
of  the  water  which  receives  it. 

It  is  necessary  during  the  remainder  of  the  determination  to  watch 
the  delivery  tube,  arid,  upon  the  reappearance  of  the  moisture  within 
the  vertical  arm,  to  repeat  the  heating  of  the  delivery  tube  as  already 
described.  The  moment  the  inner  wall  becomes  dry,  however,  this 
heating  should  be  interrupted. 

(rf)  Under  the  heating  effect  of  the  condensing  steam,  the  water 
within  the  beaker  will  rise  rapidly  in  temperature.  It  should  be 
stirred  from  time  to  time  and  its  temperature  noted,  and  when  it 
reaches  a  temperature  as  far  above  the  temperature  of  the  room  as 
its  initial  temperature  was  below,  it  should  be  removed  from  its  posi- 
tion beneath  the  delivery  tube.  To  determine  the  amount  of  steam 
which  has  been  condensed  in  the  process  of  heating  the  liquid  through 
this  range  of  temperature,  the  beaker  is  weighed  again. 

(e)  The  formula  for  the  computation  of  the  results  of  this  experi- 
ment is  as  follows : 

V=W  (if  -  Q  -  S  (100  -  Q 
S  - 

In  this  equation,  W  is  the  mass  of  water  in  the  beaker,  S  the  mass 
of  the  condensed  steam  (both  in  grams),  and  t'  —  t  is  the  rise  of  tem- 
perature caused  by  the  condensation  of  the  latter. 

The  following  table  contains  the  heat  of  vaporization  of  various 
liquids : 

TABLE. 
THE  HEAT  OF  VAPORIZATION  OF  VARIOUS  LIQUIDS. 


Alcohol  (ethyl)     . 

208-92  calories 

Chloroform  .     . 

91-11 

Ammonia  (NH3)    . 

294-21  (at  7°-8) 

Ether  (C4H10)  . 

23-95 

Benzol     .... 

93-45 

Iodine      .     .     . 

62-00 

Bromine  .... 

45-60 

Mercury  .     .     . 

91-70  (at  0°) 

Carbon  dioxide 

56-25  (at  0°) 

Sulphur  dioxide 

58-49 

Carbon  disulphide 

86-67 

Water      .     .     . 

535-90 

174  THE  OUTLINES   OF  PHYSICS 


CHAPTER  XVIII 

PHENOMENA  ACCOMPANYING  FUSION  AND  LIQUEFACTION 

158.  Changes  of  Volume  due  to  Fusion.  —  When  a  solid 
body  is  melted  it  undergoes  a  change  of  volume.      Sub- 
stances may  be  divided  into  two  classes  according  to  the 
nature  of  this  change.    To  the  first  class  belong  substances 
the  volume  of  which  is  decreased  by  fusion.    The  chief 
member  of  this  class  is  water.     The  second  class,  which 
contains  by  far  the  larger  number  of  substances,  possesses 
a  larger  volume  in  the  melted  than  in  the  solid  state.    The 
character  of  these  changes  may  be  readily  shown  by  means 
of  the  following  experiment : 

159.  EXPERIMENT  42. —  Changes  of  Volume  resulting  from  the 
Fusion  of  Paraffin  and  of  Water. 

Apparatus : 

(1)  Two  pieces  of  glass  tubing  50  cm.  long  and  about  0*3  cm.  or 
0-4  cm.  of  inner  diameter. 

(2)  Two  beakers  each  containing  about  500  cm.8  and  a  ther- 
mometer. 

(3)  Some  crushed  ice  and  salt. 

(4)  A  small  piece  of  paraffin  and  about  50  cm.3  of  mercury. 
Procedure : 

(a)  One  end  of  each  glass  tube  is  heated  in  the  flame  of  a  blast 
lamp  or  of  a  Bunsen  burner  until  it  closes.  It  is  then  blown  into  a 
bulb  about  2  cm.  in  diameter.  Care  should  be  taken  that  the  walls 
of  this  bulb  are  not  too  thin.  After  the  glass  has  cooled,  small  chips 
of  paraffin  are  dropped  into  one  of  the  bulbs  until  the  latter  is  about 
half  full.  The  bulb  is  then  carefully  heated  in  a  flame  until  the  par- 
affin is  melted.  It  is  then  set  aside  in  a  vertical  position,  with  the 


FUSION  AND  LIQUEFACTION 


175 


MERCURY 


(3) 


open  end  uppermost,  to  cool.     After  the  paraffin  has  solidified  in  this 

bulb,  the  tube  is  bent  through  180°  in  a  luminous  gas  flame,  giving  it 

the  form  indicated  in  Fig.  148  (3),  and  after  it  has  again  had  an 

opportunity  to  cool,  it  is  filled  with  mercury  to  a  point  considerably 

beyond  the  elbow.    If  care  has  been 

used  in  the  bending  of  this  tube 

the  paraffin   will    not    have   been 

melted.      The   upper  end    of   the 

bulb  will  contain   a  cap  of  solid 

paraffin  below  which  the  contents 

of  the  bulb  and  tube  will  be  filled 

with    mercury.      Care    should    be 

taken  to  drive  out  all  air  bubbles 

from  the  space  between  the  mer- 

cury and  the  paraffin.     This  can  be 

done  by  continually  turning  the 

tube  and  tapping  the  outer  surface 

of  the  glass.     We  now  have  a  sim- 

ple form  of   apparatus   in   which 

every  change  in  the  volume  of  the 

paraffin  within  the  bulb  will  be 

indicated  by  a  rise  and  fall  of  the  mercury  column  in  the  bent  arm 

of  the  tube.     The  other  bulb  is  bent  into  the  same  form  as  the  one 

just  described.     It  is  then  filled  with  water  and  mercury  in  such 

a  manner  as  to  afford   the   same  conditions   as  those  which  exist 

in  the  tube  which  contains  paraffin  ;   i.e.  water  in  the  upper  portion 

of  the  inverted  bulb  with  mercury  below  it  and  extending  a  consid- 

erable distance  around  the  elbow.     Since  water  is  a  liquid  at  ordi- 

nary temperatures,  this  filling  can  readily  be   performed   after  the 

tube  has  reached  its  final  shape. 

(6)  The  two  bulbs  having  been  prepared  as  described  under  section 
(a),  it  remains  to  bring  each  of  them  to  the  melting  point  of  the  sub- 
stance which  it  contains,  to  allow  the  contents  to  pass  from  the  solid 
to  the  liquid  state,  or  vice  versa,  and  to  note  the  modification  of  the 
mercury  column  in  the  open  arm  of  each  tube.  For  this  purpose  the 
tube  containing  paraffin  is  placed  in  a  beaker  of  water  previously 
heated  to  a  temperature  of  60°  ;  a  temperature  which  is  slightly  above 
the  melting  point  of  that  substance.  It  will  be  noted  that  when  the 
temperature  of  the  surrounding  liquid  has  been  transmitted  to  the 
contents  of  the  bulb,  and  the  paraffin  begins  to  melt,  the  mercury 


FIG.  148. 


176  THE  OUTLINES   OF  PHYSICS 

rises  in  the  open  arm  of  the  tube,  showing  a  decided  expansion  as  the 
result  of  fusion.  To  bring  about  the  corresponding  phenomenon  in 
the  case  of  water,  the  other  bulb  is  placed  in  a  freezing  mixture  con- 
sisting of  crushed  ice  mingled  with  fine  salt. 

This  is  to  be  packed  around  the  bulb  in  the  other  beaker  to  such 
a  height  as  to  entirely  surround  the  water.  The  first  effects  of  sub- 
jecting this  bulb  to  the  influence  of  the  freezing  mixture  is  a  shrink- 
age, both  the  mercury  and  the  water  diminishing  in  volume.  Even 
before  the  water  begins  to  freeze,  the  downward  movement  of  the 
mercury  in  the  open  arm  of  the  tube  ceases,  and  it  begins  ta  rise. 
When  freezing  takes  place,  this  upward  movement  becomes  more 
rapid,  and  it  continues  until  every  drop  of  the  liquid  has  gone  over 
into  the  solid  state.  When  the  water  is  completely  frozen,  a  second 
reversal  in  the  motion  of  the  mercury  column  takes  place,  and  it 
begins  to  fall  again,  continuing  to  do  so  until  the  contents  of  the  bulb 
has  reached  the  temperature  of  the  freezing  mixture  with  which  it 
is  surrounded. 

(c)  Upon  removing  the  water  bulb  from  the  freezing  mixture  and 
the  bulb  containing  paraffin  from  the  hot  bath  within  which  it  has 
been  melted,  the  reverse  processes  may  be  observed. 

160.  Influence  of  Pressure  on  the  Melting  Point.  —  It  is 
a  general  law  that  substances  of  the  first  class,  namely, 
those  which  shrink  upon  fusion,  have  their  melting  points 
lowered  by  pressure,  while  substances  the  volume  of 
which  in  the  liquid  state  is  greater  than  before  fusion 
may  be  solidified  at  temperatures  above  their  normal  freez- 
ing points  by  the  application  of  pressure.  In  the  case  of 
water,  which  is  the  substance  thus  far  most  extensively 
experimented  with,  this  change  of  the  melting  point  is 
exceedingly  small.  It  amounts  to  0*007°  per  atmosphere 
of  pressure.  It  has  been  found  possible,  by  the  application 
of  very  great  pressures  (about  3000  atmospheres),  to 
lower  the  melting  point  of  ice  to  —  20°  C.  Paraffin, 
spermaceti,  and  most  wax-like  substances  belong  to  the 
second  class.  The  German  chemist  Bunsen  raised  the 


FUSION  AND  LIQUEFACTION  177 

melting    point    of    paraffin    3-6°    by   a    pressure    of    100 
atmospheres. 

161.  Phenomena  accompanying  Vaporization.  —  (a)  Change 
of  Volume  by  Vaporization.  When  a  liquid  goes  over  into 
the  gaseous  condition,  the  change  of  volume  is  very  much 
greater  than  when  it  is  converted  from  a  solid  to  a  liquid. 
Water,  for  example,  when  changed  into  steam  at  100°  C. 
increases  in  volume  in  the  ratio  of  1  to  1578.  There  is 
no  exception  to  the  statement  that  vaporization  is  accom- 
panied by  great  increase  in  volume.  The  precise  ratio  in 
each  case  can  be  determined  only  by  the  indirect  method 
of  measuring  the  density  of  the  saturated  vapor  produced 
at  the  temperature  and  pressure  in  question. 

(6)  Ebullition.  The  change  from  the  liquid  to  the  vapor 
state  takes  place  either  by  quiet  evaporation  at  any  tem- 
perature or  by  the  process  known  as  boiling  (ebullition). 
Ebullition  consists  in  the  gathering  of  vapor  particles  below 
the  surface  of  the  boiling  liquid  into  the  form  of  bubbles. 
These  bubbles  are  able  to  maintain  themselves  against  the 
pressure  to  which  they  are  subjected  only  when  a  certain 
temperature,  which  is  called  the  temperature  of  ebullition, 
has  been  reached.  At  temperatures  lower  than  this  all 
bubbles  forming  within  the  mass  of  the  liquid  are  com- 
pressed and  condensed,  but  as  the  temperature  rises,  the 
mass  of  vapor  which  constitutes  a  bubble  becomes  capable 
of  reacting  against  greater  and  greater  pressures.  Finally 
the  bubbles  are  able  to  resist  compression,  and  as  soon  as 
this  condition  of  equilibrium  is  passed,  they  grow  rapidly 
in  size  and  rise  to  the  surface.  Each  one  of  them,  as  it 
passes  through  the  surface  film,  carries  its  contents  of 
vapor  into  the  outer  atmosphere. 

The  liberation  of  these  masses  of  vapor  is  accompanied 

N 


178  THE  OUTLINES   OF  PHYSICS 

by  the  transfer  of  energy  from  the  liquid  mass  to  the 
atmosphere  above  it,  and  the  transfer  of  energy  tends  to 
keep  down  the  temperature  of  the  liquid.  If  the  tempera- 
ture fall  below  the  condition  which  has  just  been  described, 
ebullition  ceases.  The  liquid,  on  the  other  hand,  cannot 
rise  above  that  temperature,  because  the  slightest  tendency 
to  do  so  calls  forth  correspondingly  increased  violence  of 
boiling ;  so  that  the  rate  at  which  energy  is  transferred 
almost  instantly  becomes  sufficient  to  lower  the  tempera- 
ture again.  Thus  the  temperature  of  a  boiling  liquid  is 
in  a  state  of  equilibrium,  and  it  remains  constant  as  long 
as  the  pressure  to  which  the  liquid  is  subjected  remains 
constant. 

162.  Influence  of  Pressure  upon  the  Boiling  Point.  —  The 
pressure  to  which  a  liquid  is  subjected  will  obviously  alter 
the  condition  of  equilibrium  which  has  just  been  described  ; 
so  that  the  temperature  at  which  the  bubbles  formed  within 
the  liquid  mass  are  able  to  maintain  themselves  is  higher 
as  the  pressure  rises  and  diminishes  with  the  pressure. 
That  under  low  pressures  water  will  boil  at  low  tempera- 
tures, may  be  readily  demonstrated  as  follows : 

EXPERIMENT  43.  —  The  Thermal  Paradox. 

Apparatus : 

(1)  A   strong  flask  the  bottom   of  which   should   be  convex  (a 
Florence  flask). 

(2)  A  cork  well  fitted  to  the  flask. 
Procedure : 

(a)  The  flask  is  half  filled  with  water,  which  is  made  to  boil  for 
several  minutes.  After  a  sufficient  length  of  time  has  elapsed  to  drive 
out  the  air  from  the  atmosphere  above  the  level  of  the  liquid,  and 
also  to  exclude  the  air  contained  by  the  liquid  itself,  the  cork  is  in- 
serted into  the  mouth  of  the  flask  and  the  flame  is  extinguished. 


FUSION  AND  LIQUEFACTION 


179 


(6)  The  flask  is  then  inverted.  We  now  have  a  body  of  liquid  and 
an  atmosphere  consisting  altogether  of  its  vapor.  As  the  temperature 
falls  this  vapor  is  condensed  grad- 
ually, so  that  the  pressure  under 
which  the  liquid  exists  diminishes. 
By  causing  a  sudden  diminution  of 
pressure,  which  may  be  readily  done 
by  pouring  cold  water  over  the  flask, 
as  in  Fig.  149,  the  liquid  will  burst 
into  violent  ebullition.  The  result  of 
this  boiling  is  to  add  new  vapor  to  the 
inclosed  atmosphere,  when  the  boiling 
will  diminish  in  intensity.  Fresh  ap- 
plications of  cold  from  without  will 
cause  a  repetition  of  the  phenomenon, 
and  the  experiment  may  be  carried  on 
until  the  liquid  is  quite  cold.  FIG.  149. 

163.   The  Freezing  of  Water  by  its  Own  Evaporation.  —  By 

modifying  the  method  of  reducing  pressure  just  described, 
the  interesting  phenomenon  of  a  liquid  boiling  at  its 
freezing  point  may  be 
shown.  The  apparatus 
necessary  for  this  ex- 
periment consists  of  an 
air  pump  (Fig.  150), 
a  bell  jar,  a  flat  metallic 
dish  containing  a  small 
amount  of  water,  and 
a  larger  dish  of  porce- 
lain, also  very  shallow. 
The  labor  of  pumping  \j  — ^ 

may  be  greatly  reduced  ~~FIG.  iso. 

by   having    the    water 

previously  cooled  nearly  to  the  freezing  point.     To  suc- 
ceed in  the  demonstration  it  is  necessary  to  place  within 


180  THE  OUTLINES  OF  PHYSICS 

the  bell  jar  some  substance  which  will  unite  with  or  absorb 
the  aqueous  vapor  as  fast  as  it  is  formed  by  the  evapora- 
tion of  the  liquid.  The  best  drying  material  is  phosphorus 
pentoxide  (P2O6).  Very  strong  sulphuric  acid  freed 
from  water  by  boiling  may,  however,  be  used.  A  very 
convenient  form  of  apparatus  for  this  experiment  is  that 

shown  in  Fig.  151.    A  flat 
dish,  which  contains  the 
dryer,  is  surmounted  by 
a  flat  tripod  of  wire. 
FlG-  15L  Into  the  central  ring  of 

the  latter  fits  the  smaller  dish,  containing  the  water  to  be 
frozen.  The  latter  vessel  should  be  of  thin  sheet  metal 
and  about  5  cm.  in  diameter.  It  is  only  necessary  to  fill 
the  larger  dish  with  the  dryer  and  to  put  about  5  cm.3 
of  cold  water  into  the  smaller  one,  and  then  to  exhaust 
the  air  by  means  of  the  pump,  keeping  up  the  action  for 
a  few  minutes.  The  temperature  of  the  liquid  will  fall 
to  the  freezing  point,  and  just  before  it  freezes  the  liquid 
in  the  flat  dish  will  boil.  Ebullition  will  continue  vigor- 
ously even  under  the  layer  of  ice  first  formed,  and  will 
not  have  ceased  until  the  water  has  all  become  solid. 

164.   EXPERIMENT    44.  —  Relation    between    Boiling    Point    and 
Pressure. 

Apparatus  : 

(1)  Two  flasks  with  well-fitted  corks. 

(2)  Three  pieces  of  glass  tubing,  each  about  100  cm.  long  and 
0-3  cm.  to  0-5  cm.  in  diameter;  also  a  T-shaped  tube. 

(3)  A  filtering  pump  (see  Appendix  V). 

(4)  A  thermometer  reading  to  100°;  a  support;  a  Bunsen  burner  ; 
rubber  tubing. 

(5)  A  glass  containing  mercury. 

(6)  A  meter  scale. 

(7)  A  barometer. 


FUSION  AND  LIQUEFACTION 


181 


Procedure  : 

(a)  Bend  one  of  the  glass  tubes  into  the  form  abc  (Fig.  152).  Cut 
another  in  two,  and  bend  one  of  the  pieces  into  the  form  de.  Bore 
both  corks,  each  with  two  holes. 


FIG.  152. 

Set  the  apparatus  up  as  shown  in  the  figure,  connecting  the  uncut 
piece  of  tubing  (mn)  to  the  lower  end  of  the  T  tube  by  means  of  a 
few  centimeters  of  rubber  tubing.  The  right  and  left  hand  arms  of 
the  T  are  to  be  similarly  attached  to  the  filter  pump  W,  which  is 
fastened  to  the  water  faucet,  and  to  the  tube  de.  The  tube  mn}  the 


182 


THE   OUTLINES   OF  PHYSICS 


lower  end  of  which  is  to  be  immersed  in  the  glass  of  mercury,  serves 
as  a  manometer.  Before  the  corks  are  finally  inserted  in  the  flasks, 
A  should  be  one  quarter  filled  with  water.  All  joints  and  the  corks 


40cm 


20cm 


8 


FIG.  153. 


should  be  rendered  air  tight  by  the  application  of  rubber  cement,  or 
of  beeswax  and  rosin. 

(6)  Bring  the  water  in  A  to  a  temperature  of  about  95°,  then 


FUSION  AND  LIQUEFACTION 


183 


extinguish  the  flame  and  start  the  filter  pump.  Turn  on  the  water 
gradually  until  boiling  begins  in  the  flask  A.  Then  leave  the  pump 
in  action,  and  read  the  height  of  the  mercury  in  mn  and  also  the 
thermometer. 

(c)  Repeat  the  readings  of  manometer  and  thermometer  at  inter- 
vals of  about  five  minutes,  increasing  the  action  of  the  pump  from 
time  to  time  as  may  be  necessary  to  produce  ebullition.     Continue 
thus  until  the  pump  is  no  longer  capable  of  causing  the  water  to  boil. 

(d)  Find  the  height  of  the  barometer  in  centimeters. 

80.  cm. 


78.  cm. 


76.  cm. 


72.  cm. 


^ 

^ 

S* 

^ 

^ 

en 

D 
to 

S 

^ 

V) 

UJ 

cc 

S* 

S 

^^ 

^ 

> 

/ 

^ 

s^ 

"? 

1 

•EMF 

ERA 

T-URE 

8°                                          99°                                         100°                                        101 

FIG.  154. 

(e)  Plot  the  curve  of  your  results,  with  temperatures  as  ordinates 
and  the  height  of  the  mercury  in  mn,  subtracted  from  the  barometric 
reading,  as  abscissas.  Compare  your  curve  with  that  in  Fig.  153, 
which  gives  the  accepted  relation  between  boiling  points  and  pressure. 

(/)  Instead  of  reading  the  barometer  as  directed  in  section  (d), 
the  tube  a  may  be  withdrawn  from  the  flask  A,  the  water  may  be 
made  to  boil  by  the  action  of  the  flame,  and  the  thermometer  may 
be  read.  From  this  reading  the  height  of  the  barometer  may  be 
obtained  by  direct  reference  to  the  curve  in  Fig.  154.  This  is  a  small 
portion  of  the  curve  of  the  preceding  figure,  reproduced  upon  a  much 
larger  scale.  If,  for  example,  the  boiling  point  is  994°,  the  corre- 
sponding pressure  will  be  found  to  be  74-4  cm.,  which  is  the  baro- 
metric reading. 


184  THE  OUTLINES   OF  PHYSICS 

165.    Influence   of   Evaporation   upon   Temperature.  —  In 

addition  to  the  process  of  ebullition,  there  is  always  going 
on  an  escape  of  liquid  particles  into  the  atmosphere  by 
the  process  known  as  evaporation.  This  process  consists 
in  the  passage  of  individual  particles  of  liquid  through 
the  surface  film  and  out  into  the  gaseous  atmosphere 
beyond.  It  occurs  more  rapidly  at  high  than  at  low  tem- 
peratures. Evaporation  occurs  because  the  particles  of  a 
liquid  are  ever  in  motion  among  themselves.  The  more 
rapidly  the  particles  move,  the  higher  is  the  temperature. 
The  particles  of  a  liquid  do  not,  however,  all  move  with 
the  same  velocity,  and  it  is  chiefly  those  of  high  velocity 
which  escape  through  the  surface  film  in  evaporation. 
Evaporation,  therefore,  deprives  the  liquid  of  those  parti- 
cles which  possess  the  greatest  energy  of  motion,  conse- 
quently it  produces  fall  of  temperature. 

This  fact  may  be  shown  in  many  ways.  If  the  hand, 
for  example,  be  plunged  into  warm  water  and  then  with- 
drawn, the  result  will  be  a  distinct  sensation  of  chilliness 
due  to  evaporation. 

If  two  thermometers,  which  give  the  same  reading  when 
placed  side  by  side,  are  taken,  and  the  bulb  of  one  of  them 
be  wrapped  in  filter  paper,  or  other  porous  material,  and 
then  be  moistened  with  a  liquid,  the  temperature  of  which 
is  as  high  as  that  of  the  room,  or  even  higher,  a  difference 
in  the  reading  of  the  two  thermometers  will  soon  become 
noticeable.  The  one  with  a  dry  bulb  will  show  a  higher 
temperature  than  the  other.  The  rate  of  evaporation  of 
the  liquid  surrounding  the  moistened  bulb  will  depend 
upon  the  amount  of  moisture  present  in  the  surrounding 
atmosphere,  and  since  rapid  evaporation  lowers  the  tem- 
perature to  a  greater  degree,  this  comparison  of  wet  and 
dry  bulb  thermometers  affords  a  means  of  determining  the 
humidity  of  the  air. 


FUSION  AND  LIQUEFACTION  185 

A  striking  illustration  of  the  lowering  of  temperature 
by  evaporation  is  as  follows.  A  test  tube  of  water,  sur- 
rounded with  cotton  waste  or  other  porous  material  which 
has  been  well  saturated  with  ether,  is  placed  under  the 
bell  jar  of  an  air  pump,  and  the  air  is  removed.  The  re- 
duction of  pressure  hastens  evaporation,  and  a  sufficient 
amount  of  heat  is  abstracted  from  the  liquid  by  the  sur- 
rounding ether  to  reduce  the  temperature  below  the  freez- 
ing point.  In  a  few  minutes  the  water  will  freeze. 

166.  The  Spheroidal  State.  —  When  a  drop  of  water  falls 
upon  a  hot  surface,  the  temperature  of  which  is  very  far 
above  the  boiling  point  of  the  liquid,  it  does  not  come  into 
immediate  contact  with  the  surface,  as  it  would  do  if  the 
temperature  of  the  latter  were  not  so  high,  but  is  gathered 
by  the  action  of  the  surface  film  into  the  form  of  a  sphe- 
roid.    The  globule  of  liquid  thus  formed  is  separated  from 
the  surface  of  the  hot  solid  by  a  layer  of  steam.     This 
layer  of  steam  is  constantly  renewed  by  rapid  evaporation 
from  the  lower  side  of  the  drop,  and  it  issues  with  a  force 
sufficient  to  enable  it  by  its  reaction  to  support  the  drop 
out  of   contact  with  the  hot  surface.     Steam,  like  other 
vapors,  is  a  very  poor  conductor  of  heat,  consequently  the 
drop  remains  at  a  comparatively  low  temperature  (below 
its  boiling  point),  being  kept  cool  by  its  own  evaporation. 
Liquid  existing  in  this  condition  is  said  to  be  in  the  sphe- 
roidal state.     The  most  convenient  form  of  experiment  for 
illustrating  the  phenomena  connected  with  the  spheroidal 
state  is  as  follows : 

167.  EXPERIMENT  45.  — The  Spheroidal  State  of  Water. 

Apparatus : 

(1)  A  metal  plate  composed  of  some  material  which  is  capable  of 
being  heated  beyond  the  red  heat  without  being  melted.  The  best 


186  THE  OUTLINES  OF  PHYSICS 

thing  to  use  for  this  purpose  is  the  inverted  cover  of  a  platinum  cru- 
cible, or  a  piece  of  platinum  foil  carefully  flattened  and  bent  into 
slightly  concave  form  (a  piece  of  sheet  iron  will  answer,  or  a  porce- 
lain crucible  cover). 

(2)  A.  fiat  piece  of  platinum  or  sheet  iron. 

(3)  A  blast  lamp. 

(4)  A  beaker  of  water  and  a  pipette. 

Procedure : 

(a)  The  metal  plate  is  placed  upon  the  iron  ring  of  a  retort  stand, 
care  being  taken  to  have  it  as  nearly  level  as  possible.  It  is  then 
heated  to  a  bright  red  heat  from  below  by  means  of  the  blast  lamp, 
and  a  globule  of  the  liquid  is  carefully  discharged  upon  the  surface 
of  the  hot  plate.  It  will  be  seen  to  assume  at  once  the  spheroidal 
form.  The  spheroid  will  settle  over  the  lowest  point  of  the  hot  sur- 
face, where  it  will  remain  without  boiling,  wasting  away  rapidly  by 
evaporation  until  it  finally  disappears. 

(ft)  Substitute  the  flat  piece  of  foil  for  that  used  in  the.  previous 
section.  Take  a  piece  of  iron  wire,  and  plunge  the  point  of  it  into 
the  globule  of  liquid.  The  surface  film  will  make  contact  with  the 
rod  or  wire,  and  the  globule  can  then  be  moved  to  any  part  of  the 
plate.  In  this  way,  holding  the  eye  on  a  level  with  the  heated  sur- 
face, and  moving  the  globule  to  some  portion  of  the  latter  which  is 
slightly  convex,  it  will  be  found  possible  to  look  through  the  layer 

of  steam  between  the  drop  and  the 
metal,  and  thus  to  obtain  direct  vis- 
ual evidence  that  contact  between 
them  does  not  exist.  Downward 
pressure  with  the  rod  will  flatten 
the  globule  without  bringing  it  ap- 
preciably nearer  to  the  hot  surface. 
FIG  155  Figure  155  shows  a  drop  of  water 

thus  pressed  against  the  layer  of 
steam  which  supports  it  from  the  hot  surface  of  an  inverted  cruci- 
ble. The  rod  used  in  this  case  was  simply  the  pipette  by  means  of 
which  the  liquid  had  been  dropped  upon  the  metal.  The  figure, 
which  is  from  a  photograph,  shows  the  layer  of  steam  which  serves 
as  a  cushion  holding  the  liquid  and  solid  apart.  The  flattening  of 
the  drop  beneath,  caused  by  the  attempt  to  press  it  closer  to  the 
crucible,  is  very  evident. 


RELATIONS  BETWEEN  HEAT  AND    WORK         187 


CHAPTER   XIX 

RELATIONS  BETWEEN  HEAT  AND  WORK 

168.  The  Mechanical  Equivalent  of  Heat.  —  We  have 
already  spoken  of  heat  as  a  form  of  energy  consisting  of 
some  motion  of  the  individual  particles  of  a  substance 
among  themselves.  The  particles  of  a  body  do  not  come 
into  this  condition  of  motion  without  being  brought  into 
it  by  the  action  of  outside  forces.  The  transfer  of  energy 
which  takes  place  under  these  conditions  manifests  itself 
generally  by  a  rise  of  temperature.  If,  for  example,  a 
body  possessing  kinetic  energy  be  brought  to  rest  through 
impact  with  some  other  body,  a  part  of  its  energy  of 
motion  appears  to  be  lost,  because  the  body  with  which 
it  made  impact  has  not  acquired  so  large  an  amount  of 
kinetic  energy  as  the  body  which  has  been  brought  to  rest 
has  delivered  to  it. 

If  we  look  more  closely  into  the  phenomena  which 
accompany  impact,  we  find,  however,  that  both  bodies 
show  a  rise  of  temperature.  This  rise  of  temperature 
indicates  that  the  motion,  apparently  lost,  has  really  been 
transferred  to  the  particles  of  both  bodies,  throwing  them 
into  motion  among  themselves.  We  cannot  see  these 
molecular  motions,  even  with  the  aid  of  the  microscope, 
but  there  is  no  reasonable  doubt  of  their  existence.  If  we 
measure  the  rise  of  temperature  and  compute  the  heat 
energy  in  calories,  we  find  that  it  always  reaches  a  certain 
definite  amount  per  unit  of  kinetic  energy  destroyed  in 
producing  it  (Art.  174).  The  relationship  between  the 


188  THE  OUTLINES   OF  PHYSICS 

work  which  disappears  and  the  heat  energy,  measured  in 
calories,  which  its  disappearance  calls  forth,  is  termed  the 
mechanical  equivalent  of  heat.  This  transfer  of  energy, 
from  the  form  of  kinetic  energy  to  that  of  heat  energy, 
may  be  illustrated  by  numerous  familiar  examples.  The 
heat  developed  in  the  process  of  boring  a  hole  in  wood  or 
metal,  or  in  breaking  a  wire  or  rod  by  bending  it  back  and 
forth,  illustrates  this  principle.  It  was  through  observa- 
tions of  the  large  amount  of  heat  produced  in  boring  can- 
non, which  first  led  Count  Rumford,  who  was  employed 
in  the  supervision  of  such  work  by  the  king  of  Bavaria, 
to  the  conception  that  heat  was  a  mode  of  motion  and  was 
produced  by  the  expenditure  of  work.  Energy  expended 
in  resistance  to  motion,  i.e.  in  friction,  is  nearly  always 
entirely  converted  into  heat.  The  following  experiment, 
due  to  Tyndall,  illustrates  this  transfer  of  energy,  together 
with  the  reverse  process  of  converting  heat  energy  into 
energy  of  motion  : 

169.    EXPERIMENT  46.  —  Production  of  Steam  directly  from  the 
Heat  of  Friction  (Tyndall's  Experiment). 
Apparatus  : 

(1)  A  whirling  table  upon  which  is  mounted  a  brass  tube  about 
2  cm.  in  diameter  and  about  10  cm.  long.     (See  Fig.  156.) 

(2)  A  cork  which 
fits  the  open  end  of 
the  tube,  and  a  wood- 
en clamp  of  the  form 
shown  in  the  figure. 
Procedure  : 
(a)    The    tube    is 


FIG.  156. 

water,  and  the  upper 

end  is  firmly  closed  by  means  of  the  cork. 

(6)  The  whirling  table  is  put  into  motion,  the  tube  being  held  in 
the  jaws  of  the  clamp  with  sufficient  pressure  to  produce  as  large  an 


RELATIONS  BETWEEN  HEAT  AND    WORK         189 

amount  of  friction  as  can  be  obtained  without  causing  the  belt  to 
slip.  After  driving  the  tube  rapidly  for  a  few  minutes,  a  sufficient 
amount  of  heat  will  be  developed  to  cause  the  water  to  boil.  Steam 
will  be  produced,  and  the  pressure  will  rise  until  the  cork  is  blown 
from  the  mouth  of  the  tube.  Here  we  have  the  transfer  of  the  energy 
of  motion,  through  the  agency  of  friction,  into  heat  energy.  The 
result  is  a  rise  of  temperature,  together  with  a  change  of  state  from 
the  liquid  to  the  gaseous  form.  The  energy  of  motion  of  the  cork  is 
far  from  being  the  equivalent  of  the  energy  of  the  work  done  in  driv- 
ing the  whirling  table,  because  a  large  portion  of  the  heat  energy 
evolved  is  transferred  to  surrounding  bodies,  producing  molecular 
motions  in  them  and  rise  of  temperature. 

170.  Changes  of  Temperature  as  the  Result  of  Compression 
and  Expansion.  —  One  of  the  many  ways  in  which  energy 
may  be  stored  is  by  the  compression  of  a  gas  in  a  closed 
vessel.  A  gas  possesses  perfect  elasticity  of  volume.  It 
tends  to  react,  therefore,  and  when  it  is  allowed  c=— -^ 
to  escape  it  is  capable  of  doing  work.  One  of 
the  phenomena  which  accompanies  this  process 
is  the  rise  of  temperature  as  the  result  of  the 
compression,  and  a  fall  of  temperature  when  the 
gas  is  released  and  allowed  to  expand  again. 
The  rise  of  temperature  of  a  gas  in  process  of 
compression  may  be  readily  observed  in  the  case 
of  the  small  compression  pumps  used  for  inflating 
the  pneumatic  tires  of  bicycles.  The  tube  which 
connects  the  pump  with  the  tire  grows  very  Rff* 
warm,  and  in  some  cases,  where  the  pumping  is  /  .  \ 
rapid,  it  becomes  too  hot  to  be  held  in  the  hand.  1 

The  heating  due  to  compression  may  readily    FlG-ly'- 
be  illustrated  by  means  of  the  simple  form  of  compression 
pump  shown  in  Fig.  157.     This  is  an  air  pump  with  valves 
reversed.     A  convenient  method  is  that  described  in  the 
following  experiment : 


190 


THE  OUTLINES   OF  PHYSICS 


FIG. 158. 


171.    EXPERIMENT   47. —  Heat  developed  by  the  Compression  of 
a  Gas. 

Apparatus  : 

(1)  A  simple  compression  pump. 

(2)  A  thermopile  and  galvanometer.      (See  Appendix  VI;   also 
Chapter  XXXII.) 

Procedure : 

(a)  Fit  the  nozzle  of  the  pump  into 
the  hollow  cone  of  the  thermopile,  as 
shown  in  Fig.  158. 

(ft)  Connect  the  thermopile  to  the 
galvanometer,  and  set  the  former  up 
in  the  position  shown  in  the  figure, 
with  the  pump  inserted  vertically  in 
the  upper  cone.  By  crowding  the  noz- 
zle of  the  pump  firmly  down  into  the 
cone,  a  small  volume  of  air  is  trapped 
above  the  upper  face  of  the  pile.  This  air  will  be  compressed  by 
the  action  of  the  pump. 

(c)  Work  the  pump  rapidly,  but  with  care,  observing  the  galva- 
nometer.   It  will  be  found  that  the  latter  responds  to  every  stroke,  and 
that  the  deflection  is  in  the  direction  which  corre- 
sponds to  the  heating' of  the  upper  face  of  the  pile. 


172.  The  Fire  Syringe,  —  Another  form 
of  apparatus  for  the  demonstration  of  the 
heat  produced  in  compressing  a  gas  is 
the  fire  syringe.  This  is  simply  a  small 
compressing  pump  without  valves  (Fig. 
159).  The  experiment  consists  in  plac- 
ing a  shred  of  gun  cotton  (not  more  than 
will  go  loosely  into  the  bottom  of  an 
ordinary  thimble)  in  the  bottom  of  the 
cylinder  of  the  syringe.  The  piston  is 
then  inserted,  and  is  driven  suddenly 
downwards.  If  the  stroke  be  sharp  and 
vigorous,  the  heat  generated  will  ignite 


FIG.  159. 


RELATIONS  BETWEEN  HEAT  AND    WORK 


191 


the  gun  cotton  explosively,  with  a  puff  of  smoke.  The 
result  does  not  follow  a  slow  stroke,  because  of  the  ra- 
pidity with  which  the  heat  is  imparted  to  the  walls  of  the 
cylinder. 

173.    EXPERIMENT  48.  —  Cooling  by  the  Expansion  of  a  Gas. 

Apparatus  : 

(1)  The  compression  pump  described  in  Exp.  46  (Art.  169). 


FIG.  160. 

(2)  The   metal  reservoir  which   is  usually  furnished  with  such 
pumps. 

(3)  The  thermopile  and  galvanometer. 
Procedure  : 

(a)  Attach  the  pump  to  the  reservoir,  by  the  opening  in  the  side 
of  the  latter. 


192 


THE  OUTLINES   OF  PHYSICS 


(b)  Connect  the  thermopile  to  the  galvanometer,  and  remove  the 
cone  from  one  face  of  the  former.     Set  up  the  pump  and  reservoir  as 
shown  in  Fig.  160,  and  place  the  thermopile  close  in  front  of  the 
nozzle. 

(c)  Fill  the  reservoir  with  air  by  several  rapid  strokes  of  the  pump. 

(d)  Open  the  stopcock  S  and  note  the  deflection  of  the  galvanome- 
ter, which  will  be  such  as  to  indicate  a  cooling  of  the  face. 


174.  The  Mechanical  Equivalent  of  Heat.  —  The  first  ex- 
perimenter to  measure  the  exact  amount  of  heat  energy  in 
calories,  produced  by  the  expenditure  of  a  definite  amount 
of  work,  was  the  English  physicist  Joule.  The  principle 
of  one  of  his  forms  of  apparatus  is  shown  in  Fig.  161. 


FIG.  161. 

The  two  weights  mv  m2  fall  through  measured  distances 
under  the  action  of  gravity.  They  turn  a  paddle  within 
the  calorimeter  (7,  thus  stirring  and  thereby  warming  the 
water  which  the  latter  contains.  The  rise  in  the  tempera- 
ture of  the  water  multiplied  by  its  mass  gives  the  heat 
developed.  Joule  measured  the  work  done  by  the  falling 
weights  in  foot-pounds,  the  water  in  pounds,  and  tempera- 
ture in  degrees  of  the  Fahrenheit  scale. 

He  found  that  772  foot-pounds  were  expended  to  warm 


RELATIONS  BETWEEN  HEAT  AND   WORE         193 

one  pound  of  water  one  degree.  Translated  into  scientific 
terms,  i.e.  into  those  of  the  C.G.S.  system  of  units,  this 
means  that  to  produce  one  calorie  of  heat  (to  raise  1  gram 
of  water  1°  centigrade),  about  42,000,000  ergs  of  energy 
must  be  exerted.1 

i  Very  large  numbers  of  this  kind  are  more  conveniently  written  in 
the  form  4-2  x  107. 


194  THE  OUTLINES   OF  PHYSICS 


CHAPTER   XX 

TRANSMISSION   OF  HEAT 

175.  Conduction,  Convection,  and  Radiation.  —  There  are 
three  methods  by  which  heat  is  transferred.     In  the  first 
of    these    the   motions  which  constitute    heat  energy  are 
imparted  gradually,  from  layer  to  layer,  of  the  substance 
in  the  path  along  which  transmission  takes  place.     In  the 
second,  energy  is  carried  by  means  of  a  current,  or  stream 
of  gas,  or  liquid.     In  the  third  method  (radiation),  heat 
energy  is  transmitted  at  a  very  high  velocity  by  means  of 
a  wave  motion. 

The  phenomenon  of  conduction  may  be  illustrated  by 
means  of  the  following  simple  experiment : 

176.  EXPERIMENT  49.  —  Relative  Conducting  Powers  of  Copper, 
Iron,  and  Glass. 

Apparatus : 

(1)  A  rod  or  tube  of  glass,  an  iron  rod,  and  a  copper  rod.     These 
should  be  nearly  of  the  same  diameter. 

(2)  A  metal  dish  containing  paraffin,  a  Bunsen  burner,  and  a  gas 
burner  with  a  flat  flame.     [The  ordinary  "batswing"  or  "fishtail" 
burner.] 

(a)  Melt  the  paraffin,  and  apply  it  by  means  of  a  brush  or  cloth  to 
each  of  the  rods  which  have  been  previously  warmed  in  the  Bunsen 
flame.  Then  lay  the  rods  aside  to  cool  to  the  temperature  of  the 
room. 

(6)  Clamp  the  rods  in  a  horizontal  position  side  by  side,  as  shown 
in  Fig.  162.  [The  inconvenience,  arising  from  the  difference  in  their 
diameters,  may  most  readily  be  overcome  by  mounting  each  one  in  a 


TRANSMISSION  OF  HEAT 


195 


cork,  and  then  bringing  the  clamps  to  bear  upon  the  corks  and  not 
directly  upon  the  rods  themselves.] 

(c)  Light  the  batswing  burner,  and  bring  it  carefully  towards  the 
exposed  ends  of  the  rods  with  the  plane  of  the  flame  parallel  to  the 
vertical  plane  in  which  these  ends  lie.  Move  the  flame  up  until  all 
three  rods  are  within  it. 

(d)  Note  the  following  points : 

(1)  The     transfer     of     heat 
through  the  rods  is  a  slow  pro- 
cess. 

(2)  The   rate   at  which    the 
melting  of  the  paraffin  extends 
from  the  flame  outward  is  most 
rapid  in  the  copper,  and  is  much 
slower    in    glass    than    in    the 
metals. 

(e)  After  a  considerable  time 
the  distribution  of  temperatures 
in    the    three    rods    will    have 
reached  a  permanent  condition ; 
that  is   to   say,  the  position  of 
the  limit  of  the  melted  paraffin 
upon  each  rod  will  have   come 
to  rest.     Note  that  the  position 
which  is  thus  reached  is  furthest 
from  the  flame   in  case   of  the 
copper,  less  in  the  iron,  and  least 
in  the  glass. 

It  is  evident  that  in  order  to  maintain  those  portions  of  the  rods 
which  are  above  the  temperature  of  the  room,  at  that  temperature 
permanently,  in  spite  of  the  fact  that  heat  energy  is  being  continually 
given  off  from  the  surface  of  the  rods  to  the  surrounding  air,  a  trans- 
mission of  heat  energy  from  the  flame  outward  must  continue  to  take 
place.  The  amount  of  heat  transferred  will  necessarily  be  greatest  in 
those  materials  which  are  delivering  the  largest  amount  of  heat 
energy  to  the  surrounding  atmosphere,  and  least  in  those  which  are 
losing  the  least  heat.  Evidently  the  copper  rod  is  the  one  which 
loses  the  most,  because  a  greater  portion  of  it  is  heated  above  the 
temperature  of  the  room  than  in  case  of  the  others. 


FIG.  162. 


196 


THE  OUTLINES  OF  PHYSICS 


This  property  of  transferring  heat  is  called  conductivity.  Of  the 
three  substances  experimented  with,  copper  is  the  best  conductor, 
glass  by  far  the  poorest.1 

177.    EXPERIMENT  50.  —  Conductivity  of  Liquids. 

The  conductivity  of  liquids,  with  the  exception  of  mercury,  is  very 
much  smaller  than  that  of  most  solids.  How  very  slowly  liquids  con- 
vey heat  may  be  shown  as  follows  : 

Apparatus : 

(1)  A  funnel,  or  a  bottle  without  a  bottom,  through  the  neck  of 
which  is  inserted  a  glass  tube  ending  in  a  bulb,  as  shown  in  Fig.  163. 

(2)  A  small  quantity  of  benzine. 
Procedure : 

(a)  The  funnel  or  bottle  is  mounted  vertically  as  shown  in  the 
figure,  the  bulb  of  the  glass  tube  which  it  contains  being  a  few  milli- 
meters below  the  level  of  the  mouth. 

(&)  Water  is  poured  into  the  fun- 
nel until  it  rises  high  enough  to 
nearly  cover  the  bulb.  The  flame  of 
the  Bunsen  burner  is  applied  to  the 
surface  of  the  latter  so  as  to  slightly 
warm  it,  and  the  lower  end  of  the 
glass  tube  is  then  inserted  in  a 
beaker  of  water.  In  consequence 
of  the  heating  of  the  bulb  a  small 
amount  of  air  will  have  been  ex- 
pelled, and  when  this  cools  again 
water  will  rise  in  the  tube.  If  the 
bulb  was  not  too  strongly  heated, 
this  liquid  column  will  come  to  rest 
at  a  point  below  the  neck  of  the  fun- 
nel or  bottle,  and  the  bulb  will  then 
serve  as  a  simple  form  of  air  ther- 
mometer. 

(c)  Add  water  to  the  funnel  until 


FIG.  1G3. 


1  The  quantitative  study  of  thermal  conductivity  is  beyond  the  range 
of  the  experiments  given  in  this  book.  For  a  description  of  the  methods 
by  which  such  measurements  are  made,  see  Preston's  Theory  of  Heat, 
p.  605,  etc. 


TRANSMISSION   OF  HEAT  197 

the  same  is  brimming  full,  in  which  condition  there,  should  be  a 
depth  of  liquid  over  the  bulb  of  three  or  four  millimeters.  From  a 
very  small  flask  or  bottle  pour  about  a  cubic  centimeter  of  benzine 
upon  the  surface  of  the  water  in  the  funnel  and  ignite.  The  benzine 
will  burn  freely  and  will  generate  much  heat. 

(d)  Watch  the  liquid  column  in  the  air  thermometer.  It  will  be 
found  that  the  latter  remains  almost  completely  stationary  in  spite  of 
the  fact  that  the  layer  of  liquid  which  separates  it  from  the  flame  is 
very  thin.  It  follows,  therefore,  that  water  is  a  very  poor  conductor 
of  heat.  The  demonstration  of  the  conductivity  of  gas  is  a  more 
difficult  matter.  It  has  been  found,  however,  that  gases  conduct  heat 
even  more  slowly  than  liquids  do. 

178.  Thermal  Conductivity  a  Slow  Process.  —  The  chief 
characteristic  of  thermal  conductivity,  as  compared  with 
other  methods  by  which  heat  energy  is  transferred,  is  the 
slowness  with  which  it  takes  place.  A  striking  example 
of  this  occurs  in  the  distribution  of  temperatures  in  the 
earth's  crust.  Geologists  have  been  much  interested  in 
measuring  the  temperatures  at  different  depths  below  the 
surface  of  the  earth  by  means  of  instruments  placed  in  the 
shafts  of  mines,  and  also  in  the  narrower  bore  holes  which 
are  often  carried  to  great  depths  in  searching  for  oil,  gas, 
etc.  By  means  of  the  thermo-element  and  of  other  elec- 
trical devices,  it  is  possible  to  make  records  of  the  tem- 
peratures in  such  localities,  within  the  crust  of  the  earth, 
day  by  day  for  very  long  periods  of  time,  and  it  has  been 
found  that  the  heat  of  the  summer  weather  upon  the 
surface  of  the  earth  penetrates  surely,  but  very  slowly 
indeed,  into  the  interior.  At  a  distance  of  several  hundred 
feet,  for  example,  the  hottest  days  may  be  found  to  occur 
not  in  midsummer  but  several  months  later,  the  fluctua- 
tions of  heat  and  cold  being  reproduced,  although  with 
greatly  diminished  range  of  temperature  within  the  rock 
masses  below.  The  greater  the  distance  from  the  surface, 


198  THE  OUTLINES  OF  PHYSICS 

the  longer,  will  be  the  time  which  must  elapse  before  the 
effect  of  a  hot  spell  of  weather,  for  instance,  will  make 
itself  felt,  and  the  smaller  will  be  the  variations  of  tem- 
perature. 

179.  Convection.  —  If  the  condition  of  the  air  surround- 
ing any  heated  body  be  observed,  it  will  be  found  to  be 
in  motion.     Heated  air  rises  from  the  surface,  and  other 
currents  of  cooler  air  come  in  to  take  its  place.     These 
are  called  convection  currents.     Since  air  possesses  thermal 
capacity,  the  result  of  this  circulation  is  that  each  molecule 
of  the  moving  gas  carries  away  with  it  a  certain  definite 
amount  of  energy  which  it  has  obtained  by  contact  with 
the  hot  surface. 

Convection  currents  occur  in  liquids  also,  and  their 
presence  may  be  shown  in  a  variety  of  ways.  The  follow- 
ing experiment  is  one  of  the  best  adapted  to  this  purpose, 
and  is  easily  performed,  provided  a  storage  battery  or 
other  source  of  electrical  current  is  available  : 

180.  EXPERIMENT  51. — Convection  Currents  in  a  Liquid. 

Apparatus  : 

(1)  A  cell  consisting  of  two  plates  of  glass  clamped  between  a 
piece  of  rubber  tubing  as  described  in  Appendix  VII. 

(2)  A  short  piece  of  fine  platinum  wire  or  iron  wire,  also  some 
heavier  copper  wire. 

(3)  A  storage  battery  of  two  or  three  cells,  or  a  primary  battery 
capable  of  giving  a  considerable  current. 

(4)  A  small  amount  of  colored  water  (a  solution  of  an  aniline  dye 
will  do,  or  even  a  few  drops  of  ink) . 

Procedure : 

(a)  From  the  platinum  wire  make  a  spiral  coil  of  the  form  shown 
in  Fig.  164,  and  of  such  size  as  to  fit  the  cell.  In  the  figure,  db  and 
dc  are  pieces  of  the  copper  wire  bent  as  shown,  and  the  ends  set 
through  two  small  corks,  which  should  be  slightly  greater  in  diam- 


TRANSMISSION  OF  HEAT 


199 


eter  than  the  inner  thickness  of  the  cell.  At  b  and  c  join  the  ends 
of  the  coil  e,  either  by  soldering  or  by  wrapping  the  ends  of  the 
platinum  or  iron  wire  snugly  around  the  copper  wire. 

Place  this  arrangement  in  the  cell 
with  the  coil  as  near  the  bottom  and  as 
well  centered  as  possible.  It  will  be 
held  in  place  by  the  two  corks,  which 
are  to  be  crowded  in  between  the  glass 
plates  at  the  top  of  the  cell  when  the 
adjustment  is  made. 

(5)  Nearly  fill  the  cell  with  water, 
and  by  means  of  a  pipette  introduce 
at  the  bottom  a  layer  of  coloring 
.matter  (water  tinted  with  red  ink). 
This  layer  should  be  about  1  cm.  in 
depth.  If  this  operation  be  delicately  performed,  there  will  be  a 
sharply  marked  line  between  the  clear  and  the  stained  liquid. 

(c)  Connect  the  terminals  of  the  wire  coil  with  the  poles  of  the 
battery.  The  result  will  be  to  heat  the  wire  to  a  temperature  con- 
siderably above  that  of  the  surrounding  liquid.  Particles  of  liquid 
which  are  in  contact  with  the  metal  will  receive  heat  from  the  same, 
will  expand,  and  owing  to  their  diminished  density  will  rise  toward 
the  surface  of  the  liquid  within  the  cell.  These  will  be  replaced  by 
cold  particles  from  the  layers  of  liquid  at  the  bottom  of  the  cell. 
These  in  turn  having  been  heated  by  contact  with  the  coil,  others 
again  will  take  their  place.  Since  the  region  from  which  the  ingoing 
convection  current  comes  is  filled  with  colored  liquid,  and  since  the 
particles  which  form  this  ingoing  current  a  moment  later  constitute 
the  upward  current,  the  nature  of  the  movement  will  be  plainly  seen. 
It  will  be  seen  to  consist  of  a  movement  of  the  colored  matter  or 
liquid  through  the  mass  of  the  surrounding  water.  In  the  course 
of  a  few  minutes  a  large  portion  of  the  ink  solution  will  have  been 
transferred  from  the  bottom  of  the  cell  to  the  surface  of  the  same, 
where,  having  cooled,  it  will  begin  to  return,  falling  as  a  slow  current 
on  either  side  along  the  walls  of  the  vessel.  It  will  be  seen  by  means 
of  this  experiment  that  in  convection  we  have  a  circulatory  movement 
of  the  liquid  or  gas,  the  liquid  particles  moving  in  closed  curves  and 
carrying  heat  energy  with  them  each  time  from  the  surface  of  the 
coil  to  the  cold  regions  lying  at  a  distance  from  the  same.  That  con- 


200 


THE  OUTLINES  OF  PHYSICS 


vection  currents  serve  to  transfer  heat  may  be  shown  in  the  following 
manner : 

181.    EXPERIMENT  52.  —  The  Cooling  of  a  Heated  Body  in  Air  and 
in  Vacuo. 

Apparatus  : 

(1)    An  air  pump  with  an  open-necked  receiver. 
•  (2)    A  small  test  tube  which  will  pass  easily  into  the  neck  of  the 
receiver. 

(3)  A  thermometer  reading  to  100°. 

(4)  A  clock  or  watch  indicating  seconds  of  time. 


FIG.  165. 

Procedure : 

(a)  Fit  to  the  neck  of  the  bell  jar  a  cork  containing  a  hole  of 
sufficient  size  to  admit  the  test  tube,  as  shown  in  Fig.  165,  and  make  the 
joint  air  tight  by  the  application  of  rubber  cement  or  of  rosin-beeswax 
cement.  Insert  the  thermometer  in  the  test  tube,  holding  it  in  place 
by  means  of  a  loosely  fitting  cork,  and  suspending  it  likewise  from 
above,  as  in  the  figure. 


TRANSMISSION  OF  HEAT 


201 


(6)  Smoke  the  outer  surface  of  the  test  tube,  and  fill  the  tube 
with  hot  water  to  a  height  sufficient  to  cover  the  bulb  of  the  ther- 
mometer. Place  the  apparatus  thus  adjusted  upon  the  plate  of  the 
air  pump.  At  intervals  of  sixty  seconds,  beginning  as  soon  after  the 
apparatus  has  been  arranged  as  convenient,  read  the  thermometer, 
noting  the  times  corresponding  to  each  reading.  Continue  these 
readings  of  the  thermometer  for  ten  minutes. 

(c)  Refill  the  test  tube  with  hot  water,  and  exhaust  the  bell  jar  by 
means  of  the  air  pump.  Great  care  should  be  taken  in  this  experi- 
ment to  have  the  air  pump  placed  upon  a  firm  foundation,  otherwise 
the  thermometer  will  be  endangered.  The  pump  should  be  clamped 
to  a  laboratory  table.  As  soon  as  the  vacuum  is  complete,  make  a 
new  series  of  temperature  readings  as  described  under  section  b,  begin- 
ning these  at  the  same  temperature  as  before.  The  two  sets  of  read- 
ings should  be  tabulated  side  by  side  as  follows : 

TABLE. 
CURVES  OF  COOLING. 


IN  AIR. 

IN  VACUO.I 

Time. 

Time  from 
first  reading. 

Temp. 

Time. 

Time  from 
first  reading. 

Temp. 

h.    m.     s. 

m. 

h.    m.     s. 

m. 

12  42    0 

0 

64-20° 

12  59    0 

0 

64-30° 

—  43  — 

1 

61-30 

1     0  — 

1 

62-20 

—  44  — 

2 

58-90 

—     1  — 

2 

60-40 

—  45  — 

3 

56-60 

—    2  — 

3 

58-80 

-  46  — 

4 

54-50 

—    3  — 

4 

57-20 

—  47  — 

5 

52-60 

4.  

5 

56-00 

—  48  — 

6 

50-90 

—    5  — 

6 

55-40  2 

—  49  — 

7 

49-20 

—    6  — 

7 

53-20 

—  50  — 

8 

47-70 

7  

8 

52-10 

-  51  — 

9 

46-30 

—    8  — 

9 

51-30 

—  52  — 

10 

45-00 

—     9  — 

10 

50-50 

1  Twenty  strokes  of  the  pump  between  each  reading  to  maintain  the 
vacuum. 

2  Reference  to  Fig.  166  shows  that  this  reading  was  probably  just  1°  too 
high.    The  value  54-20°  falls  upon  the  curve  ;  the  position  is  marked  by 
means  of  a  cross. 


202 


THE  OUTLINES  OF  PHYSICS 


(d)  From  the  data  obtained  plot  two  curves  upon  the  same  sheet 
of  cross-section  paper,  with  temperatures  as  ordinates  and  times  as 
abscissas.  A  comparison  of  these  will  show  that  cooling  occurs  much 
more  slowly  in  vacua  than  when  the  heated  flask  is  surrounded  by  air. 


c 

irvc. 

S  0 

F  C< 

^oli 

^g 

V 

\\ 

V 

\ 

co° 

V 

\ 

\ 

\  ' 

\ 

„ 

\ 

\ 

uj  * 

\ 

\ 

• 

\ 

\ 

\ 

\ 

\<> 

, 

s\ 

\ 

& 

^\ 

\ 

> 

- 

\, 

\ 

50° 

\ 

s 

\ 

\ 

x 

\ 

\ 

^ 

1 

s 

\ 

\ 

4i 

n. 

Tl 

VIE 
Si 

n. 

\ 

12 

n. 

FIG.  166. 

Figure  166  is  drawn  from  the  results  of  such  a  set  of  measurements. 
It  indicates  that  in  air  the  tubeful  of  water  becomes  5-4°  cooler,  at 
the  end  of  ten  minutes,  than  is  the  case  in  vacua. 

182.  Radiation.  —  The  third  method  by  which  heat 
energy  is  conveyed  through  space  is  called  radiation. 
This  term  is  applied  solely  to  the  transfer  of  energy  by 


TEANSM1SSION   OF  HEAT 


203 


means  of  a  wave  motion.  The  waves  by  means  of  which 
heat  is  thus  distributed  are  identical  in  character  with 
light  waves,  and  many  of  their  properties  will  be  con- 
sidered when  we  come  to  that  portion  of  our  subject.  Only 
those  features  which  do  not  necessitate  a  knowledge  of  the 
character  of  the  waves  themselves  will  be  taken  up  here. 

Two  of  the  most  important  facts  concerning  radiation 
are  (1)  that  it  takes  place  through  space  unoccupied  by 
ordinary  matter,  i.e.  in  vacuo,  quite  as  readily  as  in  space 
occupied  by  any  solid,  liquid,  or  gas.  (2)  That  it  takes 
place  with  enormous  velocity.  The  first  point  may  be 
illustrated  by  means  of  the  following  experiment  : 

183.    EXPERIMENT  53.  —  Radiation  in  Vacuo  and  through  Air. 

Apparatus :  w 

(1)  The  bell  jar  described  in  Experiment  52. 

(2)  A  piece  of  fine  platinum  wire  and  some  copper  wire. 

(3)  An  air  pump. 

(4)  A  battery  of  size  sufficient  to  heat  the  wire  to  incandescence. 
Procedure : 

(a)  Two  copper  wires  are  in- 
serted through  a  cork  which  fits 
the  neck  of  the  bell  jar,  and  the 
cork  having  been  inserted  in  the 
neck,  joint  is  made  air  tight  by 
the  application  of  cement.  Wires 
from  the  terminals  of  the  battery 
are  connected  through  a  switch 
to  the  outer  ends  of  these  wires. 

(6)  Take  the  platinum  wire 
by  the  ends,  and  having  laid  the 
bell  jar  on  its  side  so  as  to  gain 
easy  access  to  the  interior,  bend 
the  ends  of  the  copper  wires  as  far  apart  as  possible.  Lay  the  plati- 
num wire  across  them  as  in  Fig.  167,  and  note  whether  the  current 
suffices  to  heat  the  platinum  red  hot.  If  not,  shorten  the  distance 
between  a  and  &,  stepwise,  until  the  platinum  wire  when  laid  across 


FIG.  167. 


204  THE  OUTLINES   OF  PHYSICS 

the  copper  wires  reaches  a  dull  red  heat.  Notice  the  length  of  wire 
thus  heated,  and  after  opening  the  switch,  join  a  and  b  with  such  a 
length,  twisting  the  platinum  and  copper  wires  together  at  each  junc- 
tion. Finally  set  the  bell  jar,  with  its  piece  of  platinum  wire  hanging 
within,  upon  the  plate  of  the  air  pump. 

(c)  Close  the  switch,  thus  completing  the  voltaic  circuit,  and  note 
the  degree  of  incandescence  attained  by  the  platinum  wire. 

(d)  By  means  of  the  air  pump  exhaust  the  air  from  around  the 
wire  while  the  current  is  still  flowing  through  the  coil.    It  will  be  seen 
that  as  the  pressure  of  the  air  diminishes,  the  wire  glows  more  and 
more  brightly,  although  no  increase  in  the  current  flowing  through 
it  takes  place.     This  increase  in  temperature  is  due  to  the  fact  that 
with  the  removal  of  the  air  from  around  the  wire  the  transfer  of  heat 
from  the  coil  to  the  walls  of  the  bell  jar  by  convection  diminishes  in 
rapidity.     Upon  readmitting  the  air  to  the  bell  jar,  after  exhaustion 
has  been  carried  as  far  as  is  practicable,  a  striking  diminution  in  the 
brightness  of  the  coil  will  become  noticeable. 

This  experiment  is  not  a  perfect  demonstration  of  the  fact  that 
radiation  takes  place  in  a  vacuum,  for  the  reason  that  the  vacuum 
produced  by  mechanical  air  pumps  is  never  complete.  In  the  much 
higher  vacua  obtained  by  means  of  mercurial  air  pumps,  namely,  in 

vessels  the  air  in  which  has  been  reduced  to - of  its  original 

100,000,000 

mass,  however,  radiation  is  still  found  to  go  on  with  un diminished 
intensity.  The  fact,  moreover,  that  heat  reaches  us  from  the  sun 
through  more  than  93,000,000  miles  of  intervening  space  devoid  of 
gas,  affords  much  more  complete  evidence  of  the  fact  that  radiation 
does  not  depend  upon  the  presence  of  a  gaseous  medium,  than  can  be 
obtained  from  any  laboratory  experiment. 

It  will  be  seen,  when  we  come  to  consider  the  matter  of  light  waves, 
that  the  statement  made  above,  with  reference  to  the  transfer  of  energy 
through  space  devoid  of  matter,  needs  qualification.  Since  waves  pene- 
trate all  parts  of  the  known  universe,  we  have  to  assume  the  presence 
everywhere  of  a  medium  which  is  called  the  luminiferous  ether. 

184.  EXPERIMENT  54.  —  The  Rapidity  of  Heat  Transmission  by 
Radiation  and  by  Conduction. 

Apparatus  : 

(1)  The  thermopile  and  galvanometer. 

(2)  A  copper  or  iron  rod  as  nearly  as  possible  of  same  diameter  as 


TRANSMISSION  OF  HEAT 


205 


shown  in   Fig.   168.     Connect  the 


the  face  of  the  thermopile  and  about  20  cm.  long.     One  end  of  this 
rod  must  be  cut  squarely  and  smoothly  off  at  right  angles  to  its  length. 

(3)  A  luminous  gas  flame  (without  chimney). 

(4)  A  block  of  ice. 
Procedure  : 

(a)  Set  up  the  apparatus  as 
thermopile  with  the  galvanome- 
ter, and   place  the   copper  bar 
with  its  smooth  end  in  contact 
with  one  face  of  the  former. 

[This  face  of  the  thermopile, 
from  which  the  cone  has  been 
removed  to  admit  the  bar,  may 
be  protected  from  draughts  of  air  by  a  wrapping  of  adhesive  tape.] 

(b)  When  the  galvanometer  needle  has  come  to  rest,  bring  the  gas 
flame  under  the  free  end  of  the  bar.     Note  roughly,  by  counting,  how 
many  seconds  elapse  before  an  appreciable  deflection  of  the  galvanome- 
ter indicates  the  arrival  of  heat  at  the  end  of  the  bar  which  touches 
the  face  of  the  thermopile.     Remove  the  flame  and  notice  that  the 
effect  on  the  galvanometer  continues  to  increase  for  a  considerable 
time  after  the  free  end  of  the  bar  has  begun  to  cool. 

(c)  After  equilibrium  has  again  established  itself  (i.e.  after  the 
bar  has  had  time  to  cool  throughout)  repeat  section  (ft),  removing  the 
flame,  however,  after  half  the  interval  necessary  to  produce  the  first 
effect  upon  the  galvanometer.     Note  the  result  and  compare  with  b. 


FIG.  168. 


FIG.  169. 


206  THE  OUTLINES   OF  PHYSICS 

(d)  Repeat  (6),  using  the  block  of  ice  at  the  free  end  of  the  bai- 
rn stead  of  the  flame. 

(e)  Remove  the  bar  and  place  the  cone  on  the  pile.     Set  up  a 
wooden  screen  (Fig.  169)  100  cm.  from  the  face  of  the  pile,  and  behind 
it  the  gas  flame.     Remove  the  screen  suddenly  and  note  that  the 
galvanometer  begins  to  show  the  effect  of  the  exposure  instantly. 

185.  Influence   of    the   Surface    upon    Radiation.  —  The 
intensity  of  radiation  depends  upon  the  character  of  the 
surface  (i.e.  upon  the  material  of  which  it  is  made  and 
upon  the  quality  of  the  surface  as  regards  polish,  etc.). 

It  also  depends  upon  the  temperature  of  the"  surface. 
The  former  statement  may  be  verified  as  follows : 

186.  EXPERIMENT  55.  —  Leslie's  Cube. 

Apparatus : 

(1)  A  hollow  cubical  vessel  of  sheet  metal  (Leslie's  cube),  the 
edges  of  which  are  about  10  cm.  long.     This  contains  an  opening  in 
the  center  of  one  face  through  which  it  may  be  filled  with  liquid,  and 
in  which  a  thermometer  may  be  inserted.     The  fonir  vertical  faces  of 
the  cube  should  be  treated  as  follows : 

Face  1  should  be  of  bright  polished  metal,  namely,  either  nickel- 
plated,  or,  if  the  cube  be  made  of  brass  or  copper,  rubbed  to  a  polish. 

Face  2  should  be  smoked  with  lampblack. 

Face  3  should  be  painted  with  red  lead. 

Face  4  should  be  smoked  in  the  flame  of  a  burning  magnesium 
ribbon.  The  result  will  be  to  coat  the  metal  with  a  thin  layer  of 
oxide  of  magnesium.  (It  may  be  painted  with  zinc  white  instead  of 
being  smoked.) 

(2)  A  galvanometer  and  thermopile. 
Procedure : 

(a)  The  cube  is  filled  with  hot  water,  and  is  placed  upon  a  revolv- 
ing stand  in  front  of  the  thermopile  as  shown  in  Fig.  170.  The  stand 
must  be  at  such  a  distance  that  the  radiation  from  the  vertical  faces 
of  the  cube  may  produce  a  considerable  deflection  of  the  galvanometer 
needle. 

(&)  Present  faces  Nos.  1,  2,  3,  and  4  in  succession  to  the  face  of 
the  thermopile,  and  note  the  behavior  of  the  galvanometer.  It  will 


TRANSMISSION   OF  HEAT 


207 


be  found  that  when  the  radiation  is  that  received  from  the  lamp- 
blacked  face,  the  deflection  is  greatest,  and  when  from  the  polished 
metal  face  of  the  cube  the  deflection  is  least.  The  other  two  faces 
give  intermediate  values.  Since  these  faces  are  all  of  them  subject  to 
the  temperature  of  the  hot  water  within  the  cube  they  will  all  radiate 


FIG.  170. 

energy  to  the  face  of  the  pile  at  the  same  temperature.  The  changes 
of  temperature  which  the  cube  undergoes  during  the  progress  of  the 
experiment  will  be  extremely  small,  —  so  small  that  they  need  not  be 
taken  into  account.  It  will  be  seen  from  this  experiment  that  at  the 
same  temperature  various  surfaces  radiate  very  different  amounts  of 
heat. 

187.  Kirchhoff  s  Law.  —  The  differences  which  various 
surfaces  exhibit,  as  regards  radiating  power,  depend  upon 
what  is  known  as  Kirchhoffs  law. 

The  statement  of  this  law  is  as  follows : 

Every  body  radiates  those  waves  which  it  is  capable  of 
absorbing,  and  in  the  same  proportion. 

The  significance  of  KirchhofFs  law  will  appear  from  the 
following  illustrations : 


208  THE  OUTLINES   OF  PHYSICS 

(1)  Imagine  a   body  polished  so    as   to   be  an  almost 
perfect  mirror.     Of  the  rays  which  fall  upon  its  surface 
nearly  all,  being  reflected,  have  no  heating  effect.     Were 
the  body  a  good  radiator,  it  would  continually  give  off 
more  energy  than  it  received,  and  would  grow  colder  and 
colder  instead  of  remaining  at  the  temperature  of  its  sur- 
roundings. 

(2)  A  black  body,  on  the  other  hand,  which  absorbed 
nearly  all  the  rays  which  reached  its  surface  and  converted 
them  into  heat,  would  grow  continually  hotter  than  the 
environment,  unless  it  were  a   correspondingly  powerful 
radiator. 

The  fact  that  all  known  bodies  tend  to  approach  the 
temperature  of  their  surroundings,  instead  of  becoming 
hotter  or  colder,  affords  the  basis  for  the  law. 

That  good  reflectors  are  bad  radiators  may  be  shown  as 
follows : 


188.   EXPERIMENT  56.  —  Kirchhoff's  Law. 

Apparatus  : 

(1)  A  porcelain  crucible  containing  a   blue  or  black  trade-mark 
burned  in  the  glaze.     The  porcelain  of  Meissen  or  of  the  royal  Berlin 
potteries  have  such  a  mark.     (Any  thin-patterned  porcelain  will  do.) 

(2)  A  blast  lamp. 

Procedure  : 

(a)  Note  the  appearance  of  the  porcelain  by  reflected  light,  the 
mark  showing  dark  upon  a  bright  background. 

(&)  Heat  the  porcelain  in  the  flame  of  the  blast  lamp,  beginning 
very  cautiously  and  raising  the  temperature  gradually  until  the  whole 
piece  is  incandescent.  Note  that  the  trade-mark  glows  more  brilliantly 
than  the  rest,  so  that  the  appearance  now  is  of  a  bright  mark  upon 
a  darker  ground. 

(c)  Extinguish  the  flame  and  watch  the  return  to  the  original 
appearance. 


TRANSMISSION   OF  HEAT 


209 


189.  Radiation  and  Temperature.  —  It  has  already  been 
stated  (Art.  185)  that  the  intensity  of  radiation  depends 
upon  the  temperature.  As  the  temperature  of  the  radi- 
ating surface  rises,  the  radiation  increases,  but  much  more 
rapidly.  Its  growth  between  0°  and  80°  may  be  demon- 
strated by  means  of  the  following  experiment : 


Fia.  171. 


190.  EXPERIMENT  57.  — Increase  of  Radiation  with  Temperature. 

Apparatus : 

(1)  The  thermopile  and  galvanometer. 

(2)  A  Leslie  cube. 

(3)  Two  blocks  of  ice ;  hot  water. 

(4)  A  thermometer. 

Procedure  : 

(a)  Mount  the  thermopile  and  galvanometer  as  in  Exp.  54,  etc. 
Set  a  block  of  ice  in  front  of  each  cone  (Fig.  171).  After  equilibrium 
has  been  reached,  read  the  galvanometer. 

(6)  Replace  one  of  the  ice  blocks  by  the  Leslie  cube.  Fill  the 
cube  with  water  at  about  20°,  and  insert  the  thermometer  (Fig.  172). 
After  equilibrium  read  both  thermometer  and  galvanometer. 

(c)  Fill  the  cube  with  water  successively  at  40°,  60°,  and  80°,  and 
read  temperatures  and  deflections. 


210 


THE  OUTLINES   OF  PHYSICS 


(d)  Tabulate  your  data,  and  plot  a  curve  with  temperatures   as 
abscissas  and  deflections  as  ordinates. 


FIG.  172. 


It  will  be  found  that  the  trend  of  the  curve  is  upwards ;  i.e.  that 
the  deflection  increases  faster  than  the  temperature.  The  deflection, 
however,  is  proportional  (or  very  nearly  so)  to  the  radiation.  This 
experiment,  therefore,  serves  as  a  demonstration  of  the  statement 
made  in  Art.  189. 


PART    III --ELECTRICITY    AND     . 
MAGNETISM 


CHAPTER   XXI 
INTRODUCTION  TO  ELECTROSTATICS 

191.  The    Relation  of    Electricity  to    other    Portions  of 
Physics.  —  The  phenomena  to  be  studied  under  the  head 
of  electricity  and  magnetism  are  very  closely  related  to 
those  which  have  been  described  in  the  foregoing  chap- 
ters.    It  is  still  with  the  action  of  forces  upon  matter, 
and  with  the  expenditure,  storage,  dissipation,  and  trans- 
formation of  energy  that  we  shall  have  to  do;  but  the 
phenomena  generally  spoken  of  as  electrical  or  magnetic, 
respectively,    have    certain    features    in    common   which 
make  it  desirable   to  consider  them  in  a  separate  group 
or  class  by  themselves. 

192.  EXPERIMENT  58.  —  Electrostatic  Attraction. 

Apparatus  : 

(1)  The  wooden  support  described  in  Art.  38. 

(2)  A  strip  of  wood  about  60  cm.  long,  2  or  3  cm.  wide,  and  1  cm. 
thick. 

(3)  A  piece  of  hard  rubber  (vulcanite)  about  30  cm.  long  (an  ordi- 
nary black  rubber  ruler  or  straightedge  will  do) ;  a  glass  rod  or  tube 
about  30  cm.  long  and  2  cm.  in  diameter ;  a  catskin  or  other  piece  of 
fur ;  a  silk  handkerchief . 


212 


THE  OUTLINES   OF  PHYSICS 


Procedure:    (a)    Balance  the  wooden  strip  upon  a  pointed  wire 
which  has  previously  been  mounted  in  a  wooden  block  (Fig.  173). 


FIG.  173. 


FIG.  174. 


(&)  Rub  the  vulcanite  ruler  vigorously  with  the  catskin  and  bring 
it  near  one  end  of  the  balanced  strip,  first  above,  then  below  the  lat- 
ter, then  on  either  side.  Note  the  attractive  force  between  the  wood 

and  the  vulcanite. 

(c)  Rub  the  glass  rod 
with  the  silk  handkerchief 
and  repeat  the  operations 
described  i  n  (6) .  Note  that 
the  wood  is  attracted  to- 
wards the  glass,  although 
perhaps  not  so  strongly  as 
towards  the  vulcanite.  (It 
is  necessary  to  have  both 
glass  and  silk  quite  dry.) 

(rf)  By  means  of  a  silk 
thread,  and  a  stirrup  made 
by  bending  a  bit  of  wire 
as  shown  in  Fig.  174,  hang 
the  vulcanite  ruler,  previ- 
ously well  rubbed  with  fur, 
from  the  support.  (See  Fig. 
175.)  Bring  near  it  the 
wooden  strip,  any  metal  tool,  the  hand  itself,  in  fact  any  object  not 
previously  rubbed,  and  note  that  strong  attractive  forces  exist  between 
the  body  thus  brought  near  and  the  suspended  ruler. 

(e)  Rub  the  glass  rod  with  silk  and  repeat  operation  (d). 


FIG.  175. 


ELECTROSTATICS  213 

193.  The  preceding  experiment  (58)  affords  the  basis 
for  the  following  statement: 

Various  bodies,  such  as  vulcanite  and  glass,  can  be 
brought  by  friction  (i.e.  by  doing  ivork  upon  them)  into  a 
condition  such  that  they  attract  and  are  attracted  by  what- 
ever bodies  may  be  near  them.  This  condition  is  called 
electrification. 

An  extension  of  the  inquiry  would  lead  to  the  conclu- 
sion that  all  substances  are  capable  of  being  electrified  by 
friction,  provided  that  they  are  rubbed  with  some  material 
differing  in  nature  from  themselves ;  also  that  the  process 
of  electrification  is  always  one  which  involves  the  expendi- 
ture of  energy. 

194.  EXPERIMENT  59.  —  Electrostatic  Repulsion. 

Apparatus : 

(1)  The  support  used  in  Experiment  58. 

(2)  Two  rods  of  vulcanite  and  two  rods  or  tubes  of  glass. 

(3)  Catskin  and  silk. 

Procedure : 

(«)  Electrify  one  of  the  vulcanite  rods  by  friction  with  the  catskin, 
and*  suspend  it  as  in  the  previous  experiment.  Rub  one  of  the  glass 
rods  with  silk  and  bring  it  near.  Note  the  attraction  between  the 
two. 

(5)  Electrify  the  other  vulcanite  rod  and  bring  it  near  the  sus- 
pended rod.  Note  that  they  repel  one  another  strongly. 

(c)  Repeat  with  one  of  the  glass  rods  electrified  and  suspended. 
Note  that,  whatever  combination  may  be  made,  there  is  repulsion 
between  electrified  glass  and  electrified  glass,  and  attraction  between 
electrified  glass  and  electrified  vulcanite. 

By  means  of  experiments  of  this  kind  upon  a  great  variety  of  sub- 
stances, it  has  been  shown  that  all  bodies,  however  electrified,  fall 
into  one  of  two  classes.  They  either  repel  glass  rubbed  with  silk, 
and  attract  vulcanite  rubbed  with  fur,  or  vice  versa. 

Bodies  of  the  first  class,  i.e.  those  which  repel  glass,  are  said  to  be 


214 


THE  OUTLINES   OF  PHYSICS 


positively  charged.     Bodies  which  attract  glass,  as  above,  are  said  to 
be  negatively  charged. 

In  general,  electrified  bodies  either  attract  or  repel  each  other. 
Those  which  repel  each  other  are  said  to  be  similarly  charged ;  those 
ivhich  attract  each  other  are  said  to  be  oppositely  charged. 

195.  The  results  of  the  two  experiments  (58  and  59) 
just  described  may  be  stated  as  follows : 

(1)  Bodies,  however  electrified,  attract  neutral  bodies. 

(2)  Bodies  similarly  charged  repel  each  other. 

(3)  Bodies  oppositely  charged  attract  each  other. 

(4)  Any  charged   body,  however   electrified,  may   be 
classified    either    as    positively    charged    (or    vitreously 
charged),  or  as  negatively  charged.      In  the  former  case, 
it  repels  glass  rubbed  with  silk ;   in  the  latter,  it  attracts 
that  body. 

196.  The  Electroscope.  —  The  study  of  the  phenomena 
of  electrification  is  greatly  aided  by  the  use  of  the  elec- 
troscope.    This  is  an  instrument  de- 
signed for  the  purpose  of  indicating 
the  presence  of   an  electric  charge, 
and  of  ascertaining  whether  the  same 
be  positive  or  negative.      The  form 
generally  employed  is  that  shown  in 
Fig.  176.     It  is  called  the  gold-leaf 
electroscope,  and  it  consists  of  a  metal 
rod,  one  end  of  which  is  inserted  in  a 
glass  flask  or  receiver,  the  object  of 
which  is  to  protect  it  from  draughts 

FIG  176  °f  air'  etc*     To  tlie  lower  end  of  tnis 

rod  are  attached  two  strips  of  gold 

foil  of  equal  size.      These  hang,  side  by  side,  from  the 
lower  extremity  of  the  rod.     The  outer  end  of  the  rod, 


ELECTROSTATICS  215 

which  projects  into  the  open  air,  is  surmounted  with  a 
metal  plate  or  ball.  The  action  of  the  electroscope  is  best 
understood  by  means  of  the  following  experiment: l 

197.  EXPERIMENT  60.  —  The  Gold-Leaf  Electroscope. 

Apparatus  : 

(1)  The  electroscope  described  in  Appendix  VIII. 

(2)  Rods  of  vulcanite  and  of  glass,  a  stick  of  sealing  wax,  a  piece 
of  roll  brimstone,  a  lump  of  rosin. 

(3)  A  catskin,  a  silk  handkerchief,  a  piece  of  flannel  or  other 
woolen  cloth. 

Procedure : 

(a)  Electrify  the  vulcanite  rod  very  slightly  by  rubbing  it  with 
the  catskin.  Bring  it  into  contact  with  the  plate  of  the  electroscope 
for  an  instant,  and  remove  it.  The  gold  leaves  which  previously  had 
hung  side  by  side  now  repel  each  other.  They  stand  at  such  an  angle 
that  the  force  of  gravitation  and  the  repellent  force  between  them 
balance  one  another. 

(6)  Touch  the  plate  of  the  electroscope  with  the  finger,  and  note 
that  the  gold  leaves  immediately  come  together  into  their  original 
position. 

These  observations  (a)  and  (6)  indicate,  among  other  things,  that 
a  body  may  be  charged  by  contact  with  an  electrified  body ;  also  that 
the  charge  may  be  dissipated  by  contact  with  a  neutral  object. 

(c)  Repeat  observations  (a)  and  (6),  using  glass  electrified  by 
rubbing  with  silk. 

(d)  Bring  the  vulcanite  rod,  or  the  glass  rod  more  strongly  electri- 
fied than  before,  gradually  into  the  neighborhood  of  the  plate  of  the 
electroscope,  and  then  withdraw  it.     Watch  the'  leaves.     It  will  be 
seen  that  the  latter  begin  to  repel  each  other  while  the  electrified 
body  is  still  at  a  considerable  distance,  and  that  the  effect  increases 
as  it  is  brought  nearer  and  nearer.     As  the  rod  is  withdrawn  from 
the  neighborhood  of  the  plate,  the  leaves  come  gradually  together 
again,  and,  finally,  they  return  entirely  into  their  original  position. 
The  electroscope,  under  these  circumstances,  is  said  to  receive  a  tem- 
porary charge,  and  the  process  is  called  charging  by  induction. 

1  For  details  of  construction  of  a  simple  but  serviceable  electroscope, 
see  Appendix  VII. 


216  THE  OUTLINES   OF  PHYSICS 

In  section  (a)  of  this  experiment,  the  electroscope  received  a  per- 
manent charge,  i.e.  it  continued  to  exhibit  repulsion  of  the  gold  leaves 
after  the  removal  of  the  electrified  rod.  The  temporary  charge,  how- 
ever, exists  only  so  long  as  the  electrified  body  remains  in  the  neigh- 
borhood, and  the  effect  is  evidently  dependent  upon  the  distance 
between  the  rod  and  the  plate  of  the  electroscope. 

(e)  Bring  the  electrified  vulcanite  rod  into  the  neighborhood  of 
the  plate  of  the  electroscope  as  in  (d).  Touch  the  plate  with  the 
finger  for  an  instant;  then  withdraw  the  hand,  and,  finally,  remove 
the  electrified  rod  from  the  neighborhood.  Note  that  the  effect  upon 
the  leaves  is  now  a  permanent  one.  They  have  received  a  permanent 
charge  by  induction. 

(/)  The  electroscope  being  still  charged  as  a  result  of  the  previous 
operation,  bring  the  vulcanite  rod  near  and  watch  the  movement  of 
the  gold  leaves.  Note  that  they  move  gradually  towards  one  another 
as  if  losing  charge  upon  the  approach  of  the  vulcanite  rod,  and  that, 
when  the  latter  is  withdrawn,  they  return  to  their  former  position. 
Repeat  this  operation,  using  the  glass  rod  electrified  by  rubbing  with 
silk,  and  note  that,  in  this  case,  the  gold  leaves  are  more  and  more 
strongly  repelled  as  the  glass  rod  approaches,  and  return  to  their 
former  condition  when  the  same  is  removed. 

We  have  in  these  last  operations  a  more  complex  phenomenon. 
The  electroscope  has  a  permanent  charge  given  to  it  by  means  of 
operation  (c?),  and  in  addition  to  this  it  receives  temporary  effects 
from  the  subsequent  proximity  of  the  electrified  rods.  These  effects 
are  dependent  upon  the  character  of  the  charge  of  the  body  which  is 
brought  near  them.  A  body  negatively  electrified,  as  is  the  case  with 
the  vulcanite  rod,  produces  a  temporary  reduction  of  the  repulsion 
of  the  gold  leaves.  A  body  positively  electrified  like  the  glass  rod 
increases  the  angle  between  the  leaves  while  it  remains  in  the  neigh- 
borhood of  the  electroscope. 

198.  Further  Discussion  of  the  Results  obtained  from  Ex- 
periment 59  ;  Hypothesis  of  Two  Fluids.  —  To  explain  the 
phenomena  observed  in  the  course  of  Experiment  59,  we 
may  make  use  of  the  following  very  convenient  but  entirely 
artificial  assumption  concerning  the  nature  of  an  electric 
charge.  Let  us  suppose  that  the  electric  charge  consists  in 


ELECT R  OS  TA  TICS  217 

the  existence  upon  the  surface  of  the  electrified  body  of  an 
invisible  fluid,  the  presence  of  which  gives  the  charged 
body  the  power  of  attraction  and  repulsion,  as  described  in 
Experiment  57.  Since  there  are  two  kinds  of  charge,  pos- 
itive and  negative,  we  may  suppose  that  there  are  two  dis- 
tinct fluids  capable  of  producing  these  charges,  and  that 
these  fluids  are  present  on  the  surface  of  all  bodies.  When 
they  are  present  in  equal  quantities,  they  neutralize  each 
other,  and  the  body  in  question  shows  none  of  the  proper- 
ties of  an  electrified  body.  It  is  said  to  be  neutral  or 
unelectrified.  When  either  fluid  is  in  excess  the  body 
shows  a  static  charge  of  the  character  which  that  fluid  is 
capable  of  producing.  The  process  of  electrification,  ac- 
cording to  this  theory,  consists  in  the  separation  of  the 
two  fluids.  Whenever  two  objects  which  differ  from  one 
another  are  rubbed  together,  such  a  separation  tends  to 
take  place  and  one  of  the  objects  will  become  positively, 
the  other  negatively  charged.  (See  Experiment  61.)  This 
is  the  explanation  of  electrification  by  friction,  according 
to  the  assumption  of  which  we  are  making  use. 

In  order  to  account  for  the  phenomena  of  electrification, 
it  is  also  necessary  to  assume  that  each  of  these  two  fluids 
exerts  a  repellent  action  upon  itself,  and  that  each  attracts 
the  other.  By  means  of  this  assumption  it  is  easy  to 
account  in  an  artificial  way  for  the  phenomena  of  tempo- 
rary and  permanent  charging  by  induction,  as  well  as  for 
the  process  of  permanent  charging  and  discharging  of  the 
body  by  contact. 

199.  Explanation  of  the  Foregoing  Phenomena  by  Means 
of  the  Hypothesis  of  Two  Fluids: 

(a)  Charging  by  contact.  When  the  electrified  body  is 
brought  into  contact  with  the  plate  of  the  electroscope,  the 


218  THE  OUTLINES  OF  PHYSICS 

fluid  which  constitutes  its  charge  is  immediately  distrib- 
uted, because  of  its  repellent  action  upon  itself,  to  all  por- 
tions of  the  surface  of  the  metal  portion  of  the  instrument. 
(The  reason  why  this  distribution  is  confined  to  the  metal 
portions  of  the  electroscope  will  be  considered  in  Art.  200.) 
The  repellent  action  of  the  fluid  upon  the  leaves  of  the 
electroscope  results  in  driving  these  apart.  The  same 
repellent  forces  exist  between  all  neighboring  portions  of 
the  charged  body,  but  the  forces  of  repulsion  are  so  small, 
compared  with  the  molecular  force  between  the  particles 
of  the  metal,  that  no  appreciable  change  of  form  or  volume 
takes  place.  The  two  gold  leaves,  however,  are  not  held 
together  by  molecular  forces,  and  the  electric  forces  due 
to  the  charge  manifest  themselves  in  driving  the  leaves 
asunder.  The  sphere  of  action  of  the  molecular  forces,  as 
was  shown  in  Chapter  X,  is  exceedingly  small.  The  elec- 
trical forces  of  attraction  and  repulsion,  on  the  other  hand, 
like  that  of  gravitation,  act  at  all  distances  in  inverse  ratio 
to  the  square  of  the  distance. 

(5)  Discharge  by  contact.  Although  the  fluid,  which  is 
assumed  to  constitute  the  electric  charge,  repels  itself  and 
is  thus  driven  into  all  portions,  however  remote,  of  the  sur- 
face of  the  body  upon  which  it  exists,  it  cannot  leave  that 
body  excepting  by  traveling  along  the  surface  of  other 
bodies,  or  by  being  carried  away  by  the  latter.  The  result 
is  that  a  body  charged,  and  then  isolated  from  other  matter, 
would  remain  charged  indefinitely.  If,  however,  we  bring 
a  body  that  is  capable  of  carrying  away  the  fluid  into 
contact  with  any  portion  of  the  charged  metal,  the  fluid, 
on  account  of  its  repellent  action  towards  itself,  will  im- 
mediately flow  away  over  the  surface  of  that  body.  The 
electrified  body  thus  loses  its  charge  by  contact. 

(<?)   Temporary  charging  by  induction.     When  the  vul- 


ELECTROSTATICS  219 

canite  rod  previously  electrified  is  brought  near  to  the  plate 
of  the  electroscope,  but  not  into  contact  with  the  latter,  the 
two  fluids  already  existing  upon  the  surface  of  the  electro- 
scope in  equal  amounts  are  acted  upon.  The  fluid  of  posi- 
tive charge  is  attracted  by  the  neighboring  fluid  of  negative 
charge  upon  the  vulcanite  rod.  The  negative  fluid,  being 
similar  in  character  to  that  which  constitutes  the  charge  of 
the  vulcanite  rod,  is  repelled  and  flows  downward.  It 
takes  up  its  position  chiefly  in  the  leaves  of  the  instrument. 
The  leaves  are  therefore  repelled,  and  the  electroscope 
shows  a  temporary  charge  by  induction. 

Neither  of  the  fluids  in  this  operation  has  been  allowed 
to  escape  from  the  surface  of  the  electroscope,  nor  has  any 
charging  fluid  been  added  from 
without.  The  only  thing  that 
has  taken  place  has  been  the  re- 
arrangement of  the  fluids  upon 
the  surface  of  the  instrument. 
The  positive  charge  gathers  11 

upon  the  plate  of  the  instru-  .J  l^ 

ment  as  indicated  in  Fig.  177, 
while   the   negative  charge  is  _A_ 

driven  downward  to  the  gold 
leaves.      When   the   inducing 


body,    namely,    the   vulcanite  Fia- 177> 

rod,  is  removed,  these  fluids,  which  attract  each  other, 
return  to  their  former  distribution.  They  there  neutralize 
each  other  on  every  portion  of  the  metallic  surface,  and 
the  charge  disappears. 

(cT)  Permanent  charging  by  induction.  The  first  por- 
tion of  this  operation  is  that  described  in  the  previous  sec- 
tion. As  has  already  been  stated,  however,  it  is  necessary 
to  bring  into  contact  with  some  portion  of  the  metal  of 


220  THE   OUTLINES   OF  PHYSICS 

the  electroscope,  a  body  which  is  capable  of  conveying  the 
electric  fluid  away.  The  fluid  which  thus  escapes  is  the 
one  which  is  repelled  by  the  charge  of  the  electrified  rod. 
This  fluid  passes  off  to  the  body  of  the  operator,  and  so  to 
the  earth,  leaving  behind  an  excess  of  the  positive  charge. 
When  the  finger  is  removed  from  the  plate  of  the  electro- 
scope, and  that  instrument  is  thus  isolated,  and  when  the 
electrified  rod  is  also  removed  to  a  distance,  it  is  the  same 
as  though  a  permanent  charge  by  contact  with  a  positively 
electrified  body  has  taken  place ;  that  is  to  say,  there  is 
an  excess  of  the  positive  fluid  which  immediately  spreads 
itself  over  the  entire  surface  and  increases  the  repulsion 
of  the  leaves. 

The  reason  why,  under  these  circumstances,  the  leaves 
of  the  electroscope  are  drawn  together  when  the  electrified 
vulcanite  rod  is  brought  near  is  obvious.  Since  the  fluid 
which  constitutes  the  charge  is  positive,  it  is  attracted  by 
the  negative  charge  of  the  rod,  and  is  drawn  out  of  the 
leaves  of  the  plate,  thus  reducing  their  repellent  action 
upon  each  other.  When,  on  the  other  hand,  a  positively 
charged  body,  such  as  a  glass  rod  rubbed  with  silk,  is 
brought  near,  the  positive  charge  repels  a  like  charge  on 
the  metal  of  the  electroscope,  driving  more  of  it  down 
into  the  leaves,  and  increasing  their  repellent  action. 


CONDUCTORS  AND  NON-CONDUCTORS  221 


CHAPTER   XXII 

CONDUCTORS  AND  NON-CONDUCTORS:    ELECTRICAL 
MACHINES 

200.  Conductors  and  Non-conductors.  —  In  discussing  the 
performance  of  the  electroscope,  the  statement  was  made 
that  the  charge  imparted  to  the  body  by  contact  with 
the  electrified  body  immediately  distributed  itself  over  the 
surface  of  the  metallic  portion  of  the  instrument.  There 
is  a  distinction  in  this  respect  which  it  is  important  to 
consider. 

Some  bodies  distribute  with  great  rapidity  whatever 
electric  charge  they  may  acquire  to  all  portions  of  their 
surface.  Such  bodies  are  called  conductors  of  electricity. 
Other  substances  are  not  capable  of  thus  rapidly  conveying 
the  charge.  The  latter  are  called  non-conductors. 

The  distinction  is  not  an  absolute  one,  and  it  would 
perhaps  be  more  accurate  to  say  that  certain  bodies  are 
good,  while  others  are  bad,  conductors.  To  illustrate  the 
very  great  difference  in  this  respect  between  such  sub- 
stances as  glass  and  the  metals,  the  following  experiment 
may  be  tried : 

EXPERIMENT  61.  —  Conductors  and  Non-conductors. 
Apparatus  : 

(1)  The  gold-leaf  electroscope. 

(2)  A  naked   copper  wire   about  2  m.  long  and  a  glass  rod  or 
tube  of  the  same  length. 

(3)  Rods  of  vulcanite  and  glass,  a  catskin,  and  a  silk  handker- 
chief. 


222  THE  OUTLINES   OF  PHYSICS 

Procedure  : 

(a)  Suspend  the  copper  wire  horizontally  as  shown  in  Fig.  178, 
hanging  it  by  means  of  two  silk  threads  to  which  wire  stirrups  have 
been  attached.  One  end  of  the  rod  should  be  in  contact  with  the 
plate  of  the  electroscope.  Electrify  the  vulcanite  rod,  and  bring  it 
near  the  free  end  of  the  wire.  Note  the  effect  upon  the  electroscope. 
It  will  be  found  that  the  instrument  can  be  charged  both  by  contact 

i 

l 
I 


FIG.  178. 

and  induction,  using  the  wire  as  an  intervening  medium.  Repeat, 
using  the  glass  rod  as  a  source  of  electrification,  instead  of  the  rod 
of  vulcanite. 

(6)  Substitute  for  the  copper  wire  the  long  glass  tube,  and  attempt 
to  repeat  operation  (a).  It  will  be  found  that  the  electroscope  does 
not  respond.  Whatever  movement  of  the  gold  leaves  is  brought 
about  will  take  place  just  as  well  without  the  intervening  glass  rod 
as  with  it.  The  body  through  which  electrification  takes  place,  as 
in  the  case  of  the  copper  wire,  is  called  a  conductor,  one  through 
which  it  does  not  take  place  a  non-conductor. 

201.  Equal  and  Opposite  Charges.  —  In  electrification  by 
friction,  two  equal  and  opposite  charges  are  always  pro- 
duced ;  if  the  body  rubbed  becomes  positively  charged,  the 
body  by  means  of  which  it  is  electrified  invariably  takes 
a  negative  charge.  This  fact  may  be  demonstrated  by 
means  of  the  following  experiment : 

EXPERIMENT  62.  —  Production  of  Opposite  Charges  by  Friction. 

Apparatus : 

(1)  The  electroscope. 


CONDUCTORS  AND  NON-CONDUCTOES  223 

(2)  The  silk  and  catskin ;  also  the  glass  and  vulcanite  rods  pre- 
viously mentioned. 

Procedure : 

(a)  Charge  the  electroscope  by  induction  from  the  vulcanite  rod, 
and  test  its  condition  by  afterwards  bringing  the  rod  near,  but  not 
into  contact  with,  the  plate  several  times  and  noting  that  the  leaves 
are  drawn  together. 

(b)  Electrify  the  glass  rod  by  friction  with  the  silk  handkerchief, 
and  bring  the  handkerchief,  held  with  the  tips  of  the  fingers,  so  that 
as  small  a  portion  of  its  surface  as  possible  may  come  into  contact 
with  the  hand  and  thus  be  discharged  near  the  plate  of  the  electro- 
scope.   Note  that  the  leaves  are  drawn  together,  which  is  a  sign  of 
the  negative  charge  upon  the  handkerchief.      Bring  the  glass  rod 
itself  into  the  neighborhood  of  the  electroscope  and  note  the  diver- 
gence of  the  leaves.    It  will  be  found,  however  often  this  operation  be 
repeated,  that  the  glass  and  the  silk  handkerchief  are  always  oppo- 
sitely charged;  the  former  positively,  the  latter  negatively. 

(c)  Repeat  this  operation  using  the  vulcanite  rod  and  the  cat- 
skin.     It  will  be  found  somewhat  more  difficult  to  show  the  presence 
of  the  positive  charge  on  the  catskin  than  to  show  the  presence  of 
the  negative  charge  on  the  silk,  since  the  catskin  is  by  no  means 
so  good  an  insulator.     If,  however,  a  small  piece  of  fur  or  a  bit  of 
woolen  cloth  be  tied  to  the  end  of  the  glass  rod  and  then  be  pushed 
lightly  but  briskly  over  the  surface  of  the  vulcanite,  it  will  gather  a 
positive  charge  which  is  not  able  to  escape  on  account  of  the  poor 
conductivity  of  the  glass.     The  nature  of  its  charge  can  thus  be 
readily  demonstrated. 

The  experiment  may  be  extended  to  various  other  bodies  which 
are  not  conductors  of  electricity. 

202.  The  Electrostatic  Series.  —  The  phenomenon  of  elec- 
trification by  friction  is  not  confined  to  a  few  such  sub- 
stances as  glass  and  vulcanite.  It  is  indeed  a  perfectly 
general  property  which  may  be  stated  thus  : 

Whenever  two  bodies  not  identical  in  their  chemical  consti- 
tution and  molecular  arrangement  are  rubbed  together,  they 
become  charged,  one  of  the  bodies  assuming  a  positive  and 


224  THE  OUTLINES   OF  PHYSICS 

the  other  an  equal  negative  electrification.  In  the  case  of 
metals  and  other  good  conductors  of  electricity,  special 
precaution  must  be  taken  to  prevent  the  immediate  dissi- 
pation of  the  charge ;  in  the  case  of  poor  conductors,  the 
dissipation  is  so  slow  that  there  is  no  difficulty  in  detect- 
ing the  same. 

By  means  of  the  electroscope,  the  fact  that  a  great 
variety  of  different  bodies  can  be  electrified  by  friction 
may  be  shown.  It  is  only  necessary  for  this  purpose 
to  collect  bits  of  sulphur,  rosin,  sealing  wax,  glass, 
quartz,  etc.,  together  with  pieces  of  flannel,  silk,  paper, 
and  various  other  textile  materials  and  to  rub  these  to- 
gether pairwise,  testing  each  pair  by  bringing  first  one 
and  then  the  other  of  the  two  substances  which  have 
been  in  contact  into  the  neighborhood  of  the  electroscope. 
It  will  be  found  that  whatever  substances  be  selected, 
electrification,  more  or  less  marked,  will  result  from  rub- 
bing them  together,  and  that  the  body  rubbed  and  the  one 
with  which  it  has  been  in  contact  always  take  opposite 
charges.  By  rubbing  every  object  in  this  collection  suc- 
cessively with  every  other,  it  will  be  found  possible  to 
arrange  them  in  order,  placing  first  in  the  list  that  body 
which  is  positive  when  electrified  by  contact  with  each  and 
every  other  member  of  the  collection,  next  after  it  the 
body  which  is  positively  electrified  by  friction  with  all 
the  remaining  members,  and  so  on,  until  at  the  end  of  the 
list  is  put  that  body  which  is  found  to  be  negative  by  con- 
tact with  every  other  member  of  the  collection.  The 
properties  of  substances  in  this  regard  are,  to  a  great 
extent,  due  to  external  differences  of  structure  or  surface, 
so  that  the  series  does  not  always  take  the  same  order  at 
the  hands  of  different  observers.  The  following  is  the 
arrangement  given  by  Faraday  : 


CONDUCTORS  AND  NON-CONDUCTORS 


225 


Fur. 

Flannel. 

Ivory. 

Feathers. 

Quartz. 

Glass. 

Cotton. 


Linen. 

Silk. 

The  hand. 

Wood. 

Shellac. 

Metals. 

Sulphur. 


203.  Electrical  Machines.  —  Any  device  for  facilitating 
the  production  of  an  electrostatic  charge  is  called  an  elec- 
trical machine.  There 

are  two  classes  of  such 
machines :  those  which 
depend  upon  friction 
for  their  action,  and 
those  in  which  elec- 
trostatic induction  is 
made  use  of.  The  for- 
mer are  called  frictional 
machines,  the  latter  in- 
fluence machines. 

The  earliest  form  of 
f  rictional  machines  con- 
sisted simply  of  a  ball 
or  cylinder  of  glass 
mounted  upon  a  hori- 
zontal axis,  so  that  it 
could  be  given  a  rapid 
motion  of  rotation  by 
means  of  a  crank.  The 
hands  of  the  operator  served  as  the  rubber.  Figure  179 
shows  such  a  machine  as  depicted  by  the  Abbe*  Nollet  in 
the  eighteenth  century.1 

1  Nollet,  Lettres  sur  Vfilectricite. 


FIG.  179. 


226 


THE  OUTLINES   OF  PHYSICS 


In  later  machines  glass  disks  were  substituted  for  the 
spheres  and  cylinders,  and  a  rubber  consisting  of  silk  or 
of  undressed  leather  was  used  instead  of  the  hand.  It 
was  soon  found  that  an  application  of  an  amalgam  of 
sodium  to  the  leather  greatly  enhanced  the  activity  of 
the  machine.  Figure  180  shows  the  usual  form  given  to 
these  frictional  machines,  which,  to  distinguish  them  from 
other  types,  are  called  plate  machines.  The  essential 
parts  of  such  instruments  are  : 


FIG.  180. 

(1)  A  glass  plate  mounted  upon  a  cylindrical  axis  and 
turned  by  means  of  a  crank. 

(2)  A  pair  of  leather-faced  rubbers,  r,  which  clamp  the 
machine  near  the  periphery  of  the  glass. 

(3)  A  prime  conductor,  as  it  is  called,  which  is  a  metal 
body,  usually  cylindrical  in  shape  with  rounded  ends,  upon 
which  the  charge  from  the  glass  is  gathered  by  means  of 
a  pair  of  metal  combs,  the  teeth  of  which  come  as  nearly 
as  possible  into  contact  with  the  electrified  plate  at  a  point 
180°  distant  from  the  rubbers.     The  prime  conductor,  (7, 
and  also  the  clamp  are  supported  upon  glass  posts.     The 
post  which  carries  the  rubbers  is  generally  capped  by  a 
hollow  brass  ball,  as  shown  in  the  figure. 


CONDUCTORS  AND  NON-CONDUCTORS  227 

That  the  action  of  such  a  machine  is  similar  to  that  of 
a  glass  rod  rubbed  by  hand  with  a  silk  handkerchief, 
may  be  shown  by  testing  the  character  of  the  charge  upon 
the  prime  conductor,  and  upon  the  ball,  which  is  in  contact 
with  the  clamp.  It  will  be  found  that  the  prime  conductor 
always  possesses  a  positive  charge,  and  the  ball  a  nega- 
tive one.  This  fact  may  be  easily  ascertained  by  bringing 
a  proof  plane  l  into  contact  with  the  conductor  and  then 
into  the  neighborhood  of  the  electroscope,  previously 
charged  by  induction  from  the  vulcanite  rod.  The  result 
will  be  to  cause  the  leaves  to  diverge  more  strongly, 
which,  as  has  already  been  pointed  out,  is  indicative  of 
a  positive  charge  upon  the  proof  plane.  When  the  elec- 
troscope is  charged  as  above,  the  same  proof  plane,  if 
discharged  and  brought  into  contact  with  the  ball  of  the 
machine,  will  show  a  negative  charge  when  brought  near 
the  plate  of  the  electroscope. 

204.  The  Electrophorus.  —  The  simplest  form  of  machine 
for  electrifying  by  induction  is  the  electrophorus  (Fig. 
181).  This  consists  of  a  disk  of  solid 
metal,  about  20  cm.  in  diameter,  which 
rests  upon  a  plate  of  vulcanite,  or  other 
similar  material  which  is  capable  of 
being  negatively  electrified  by  friction. 
The  best  material  for  this  purpose  is  FlG>  181< 

hard  rubber.  To  the  middle  of  the  metal  disk  is  attached 
a  glass  handle.  Owing  to  the  irregularity  in  the  surface 
of  the  disk  and  of  the  plate  upon  which  it  rests,  contact  is 

1  Proof  plane  :  the  name  given  to  a  small  metal  disk,  2  cm.  or  3  cm.  in 
diameter,  with  a  handle  of  glass  or  vulcanite.  It  is  used,  as  above,  for 
testing  the  charge  of  bodies  which  cannot  be  easily  transported  to  the 
neighborhood  of  the  electroscope. 


228  THE  OUTLINES   OF  PHYSICS 

made  only  at  three  points,  the  remainder  of  the  disk  being 
separated  from  the  bed  of  vulcanite  by  a  thin  film  of  air. 

If  the  vulcanite  plate  be  charged  by  friction  with  the 
catskin,  and  the  metal  disk  be  laid  upon  it,  the  latter 
is  charged  by  induction,  positive  electricity  being  drawn 
to  the  under  side  of  the  plate,  as  indi- 
cated in  Fig.  182,  and  the  negative 
charge  repelled.  If  the  finger  of  the 
experimenter  is  then  brought  for  a  mo- 
ment into  contact  with  the  plate,  thus 
affording  the  repelled  charge  opportunity 
to  flow  off,  there  will  remain  an  excess  of  the  positive  charge 
which  has  been  attracted  to  the  inner  surface  of  the  disk. 
The  latter  may  now  be  raised  from  its  position  upon  the 
vulcanite  plate,  and  it  will  carry  with  it  a  strong  positive 
charge.  If  the  finger  be  brought  near  the  plate,  a  spark 
will  pass  between  the  disk  and  the  hand.  If  the  disk  be 
brought  near  the  plate  of  the  electroscope,  the  presence 
and  also  the  sign  of  the  charge  may  be  determined.  If 
the  vulcanite  plate  itself  be  brought  near  the  electroscope, 
it  will  be  found  charged  negatively ;  i.e.  in  a  manner  oppo- 
site to  that  of  the  disk. 

Since  the  disk  of  the  electrophorus  is  charged  by  induc- 
tion and  not  by  contact,  no  portion  of  the  original  charge 
existing  on  the  surface  of  the  vulcanite  plate  is  carried 
away  in  the  operation  just  described.  It  is  possible,  there- 
fore, to  return  the  disk  to  its  place  and  to  withdraw  it 
again  newly  charged,  without  having  electrified  the  vul- 
canite plate  in  the  meantime  by  friction.  This  process 
may  indeed  be  repeated  as  often  as  desired  without  in 
any  way  exhausting  the  original  charge  of  the  vulcanite. 
It  is  true,  nevertheless,  that  the  positive  charge  upon 
the  disk  after  each  charging  represents  a  certain  amount 


CONDUCTORS  AND  NON-CONDUCTORS 


229 


of  energy.  The  spark  which  is  formed  when  the  disk  is 
discharged,  for  example,  is  a  manifestation  of  the  develop- 
ment of  heat,  which  in  itself  indicates  the  expenditure  of 
energy.  The  source  of  the  energy  of  these  successive 
charges  is  the  work  done  in  withdrawing  the  charged  disk 
from  the  neighborhood  of  the  oppositely  charged  vulcanite 
plate.  As  has  already  been  pointed  out,  there  are  attrac- 
tive forces  between  bodies  oppositely  charged.  These 
forces  can  be  overcome  only  by  the  expenditure  of  energy. 
The  equivalent  of  the  energy  thus  expended  is  stored  in 
the  charged  body,  and  when  the  charge  is  distributed  it 
is  transformed  either  into  heat  energy  or  into  energy  of 
motion. 

205.  Influence  Machines.  —  Machines  of  this  type,  of 
which  the  electrophorus  is  the  simplest  form,  are  devices 
for  going  through  the  cycle  of  operations  described  in  the 
previous  article,  automatically. 


B- 


FIG.  183. 


B- 


FIG.  184. 


FIG.  185. 


FIG.  186. 


(1)  A  carrier  of  electric  'charge,  A  (Fig.  183),  corre- 
sponding to  the  disk  of  the  electrophorus,  is  brought  near 
to  a  charged  body,  B,  corresponding  to  the  vulcanite  plate. 

(2)  The  carrier  having  become  charged  by  induction, 
the  repelled  charge  is  carried  away  by  momentary  contact 
with  a  conducting  body  (Fig.  184). 


230 


THE  OUTLINES   OF  PHYSICS 


(3)  The  carrier  is  made  to  deliver  its  remaining  positive 
charge  in  part  to  a  second  charged  body,  B'  (Fig.  185), 
and  in  part  to  a  storage  reservoir  L  (Fig.  186). 

(4)  The  second  body,  B',  subsequently  induces  a  nega- 
tive charge  upon  J.,  which  is  transferred  by  a  similar  set 
of  operations  in  part  to  B,  increasing  its  original  charge, 
and  in  part  to  another  storage  reservoir.     This   process 
is  continued  indefinitely,  until  the  insulators  which  sepa- 
rate the  stored  charges  become  inadequate,  and  discharge 
takes  place. 

206.  The  Toepler-Holtz  Machine.  —  The  manner  in  which 
this  cycle  of  operations  is  performed  may  be  conveniently 
studied  by  means  of  the  Toepler-Holtz  machine  (Fig.  187). 


FIG.  187. 

This  apparatus  consists  of  two  vertical  glass  disks,  one 
of  which  is  stationary  while  the  other  revolves  in  front  of 
it.  Upon  the  back  of  the  stationary  plate  are  two  pieces 
of  tin  foil,  B,  B'  (Fig.  188).  These  correspond  to  the 
charged  bodies  B  and  B',  mentioned  in  the  preceding 
article.  Upon  the  front  of  the  revolving  plate  are  a  set 
of  equidistant  metallic  carriers,  each  consisting  of  a  small 


CONDUCTOBS  AND  NON-CONDUCTORS 


231 


disk  of  foil  surmounted  by  a  brass  button  (Fig.  189). 
Each  of  these  disks  corresponds  to  the  carrier,  A,  described 
in  Art.  205.  Imagine  the  revolving  plate  mounted  in  front 


FIG.  188. 


FIG.  189. 


of  the  stationary  plate,  and  turning  in  the  direction  indi- 
cated by  the  arrow.  Let  the  body  B  have  a  small  negative 
charge.  At  the  beginning  of  the  cycle  of  operations  one 
of  the  carriers,  A^  is  opposite  the  point  a  of  B,  and  a  sepa- 
ration of  positive  and  negative  charges  takes 
place  upon  its  surface.  It  then  comes  into 
contact  with  a  tinsel  brush  upon  the  end 
of  the  neutralizing  rod  nn,  which  is  shown 
in  Fig.  187,  and  the  repelled  (negative) 
charge  passes  away.  The  carrier  thus 
charged  positively  by  induction  is  carried 
by  the  rotation  of  the  plate  to  a  point 
opposite  bf  upon  the  other  charged  body  B1 . 
Here  it  passes  under  another  tinsel  brush, 
called  the  charging  brush,  by  means  of  which 
it  shares  its  charge  with  B'.  This  brush  is 
mounted  at  the  end  of  a  bent  metallic  arm, 
which  extends  around  the  edge  of  both  plates 
from  B1)  as  shown  in  Fig.  190.  Finally  A  passes  under 
the  collecting  comb  and  delivers  another  portion  of  its 
charge  to  the  storage  reservoir. 


FIG.  190. 


232 


THE  OUTLINES   OF  PHYSICS 


In  the  meantime  the  carrier  diametrically  opposite  to 
A  is  undergoing  a  similar  cycle  of  operations,  but  with 
opposite  charge,  whereby  the  body  B  receives  increase  in 
its  negative  electrification,  and  negative  charge  is  stored 
in  the  reservoir  upon  that  side  of  the  machine.  As  the 
machine  revolves,  and  new  pairs  of  carriers  come  opposite 
B  and  B' ,  respectively,  these  cycles  of  operations  are  con- 
tinually repeated. 

The  storage  reservoirs  of  an  influence  machine  are  two 
Leyden  jars  (Fig.  191),  the  inner  coatings  of  which  are 
metallically  connected  with  the  two  collecting  combs,  and 
likewise  with  two  sliding  rods  tipped  with  balls.  These 

„ .^  rods  are  mounted  horizontally 

with  their  common  axis  in 
front  of,  and  parallel  to,  the 
plates  of  the  machine.  The 
distance  between  the  balls 
may  be  adjusted  at  will. 

When  the  revolving  plate 
is  turned,  there  is  a  continued 
accumulation  of  positive  and 
negative  charge,  respectively,  in  the  two  Leyden  jars.  If 
the  balls  are  set  a  few  centimeters  apart,  the  attraction 
between  the  charges  becomes  so  great  as  to  overcome  the 
insulating  power  of  the  intervening  air,  whereupon  a  spark 
leaps  between  them.  This  results  in  the  partial  discharge 
of  the  machine ;  but  the  accumulation  is  repeated  until 
another  spark  passes,  and  so  on.  To  test  the  above  state- 
ment of  the  performance  of  the  Toepler-Holtz  machine,  the 
following  experiment  may  be  tried : 

207.    EXPERIMENT  63.  —  Testing  a  Toepler-Holtz  Machine. 

Apparatus : 

(1)    A  Toepler-Holtz  machine. 


FIG.  191. 


CONDUCTORS  AND   NON-CONDUCTORS  233 

(2)  The  electroscope. 

(3)  A  proof  plane. 

(4)  A  vulcanite  rod  and  catskin. 
Procedure  : 

(a)  Charge  the  electroscope  by  induction  from  the  vulcanite  rod, 
and  test  its  charge  by  noting  that  the  approach  of  the  rod  causes  the 
leaves  to  collapse. 

(b)  Put  the  machine  in  motion  in  such  a  direction  that  the  buttons 
pass  in  a  direction  from  the  charging  brushes  towards  the  metallic 
combs  of  the  conductor.     Continue  turning  until  sparks  pass  from 
between  the  terminals  when  the  latter  are  2  or  3  cm.  apart. 

(c)  Stop  the  machine  ;  then  bring  the  proof  plane  into  contact  for 
an  instant  with  one  of  the  balls  of  the  machine,  and  carry  it  into  the 
neighborhood  of  the  electroscope.     Note  the  movement  of  the  gold 
leaves.     Discharge  the  proof  plane  and  bring  it  into  contact  with  the 
arm  of  the  charging  brush  on  the  same  side  of  the  machine.     Its 
charge  thus  obtained  by  means  of  the  electroscope  ought  to  correspond 
in  sign  to  that  obtained  from  the  ball  upon  the  same  side  of  the 
machine. 

(d)  Repeat  this  test  for  corresponding  parts  upon  the  other  side  of 
the  machine. 

(e)  Test  the  electrification  of  one  of  the  carriers  before  it  reaches 
the  charging  brush,  between  the  brush  and  the  comb,  after  passing 
the  comb,  and  after  passing  the  brush  of  the  neutralizing  rod.     See 
whether  your  results  are  in  accordance  with  the  statements  of  the 
action  of  the  machine  given  in  the  previous  article. 

208.  Holtz  Machines  and  Wimshurst  Machines,  —  In  the 
influence  machine,  invented  by  Holtz  (Berlin,  1865),  of 
which  the  Toepler-Holtz  machine  is  a  modification,  the 
charged  bodies  are  simply  sectors  of  paper  fastened  to 
the  back  of  the  stationary  glass  plate.  The  carrier  is  the 
revolving  plate  itself.  Instead  of  charging  brushes,  pointed 
strips  of  paper  are  glued  to  the  paper  sectors.  These  pro- 
ject through  windows  in  the  stationary  plate  and  make 
contact  with  surface  of  the  revolving  plate.  One  form  of 
the  Holtz  machine  is  shown  in  Fig.  192. 


234 


THE  OUTLINES  OF  PHYSICS 


The  Wimshurst  machine   is  an   influence   machine   in 
which  both  plates  revolve  but  in  opposite  direction.     Each 


FIG.  192. 


plate  bears  a  series  of  metallic  carriers.  (See  Fig.  193.) 
For  a  full  discussion  of  the  action  of  this  machine,  see 
Elements  of  Physics,  Vol.  II,  p.  108. 


FIG.  193. 


ELECTRIC  CHARGE   UPON  CONDUCTORS 


235 


CHAPTER   XXIII 
DISTRIBUTION  OF  THE  ELECTRIC  CHARGE  UPON  CONDUCTORS 

209.  Electrostatic  Charges  reside  only  upon  the  Outer 
Surface  of  Bodies.  —  This  fact  may  be  illustrated  by  means 
of  the  following  experiment : 

EXPERIMENT  64.  —  Faraday's  Ice-Pail  Experiment. 

Apparatus  : 

(1)  A  cylindrical  vessel  with  an  open  mouth  of  the  general  form 
shown  in   Fig.  194.     Any  wide-mouthed   metal  can 

will  answer  for  this  purpose. 

(2)  An  electrical  machine. 

(3)  The  electroscope. 

(4)  An  insulating  stand,  or  a  plate  of  glass  or  vul- 
canite, upon  which  the  can  may  be  placed. 

(5)  A  small  metallic  ball,  or  button,  attached  to 
the  end  of  a  silk  thread,  the  other  extremity  of  which 
is  fastened  to  a  short  glass  rod. 

(6)  A  vulcanite  rod  and  a  catskin. 
Procedure  : 

(a)  Turn  the  plate  of  the  electrical  machine  in 
the  proper  direction  until  it  becomes  well  charged. 
Connect  one  terminal  to  the  earth.  If  a  frictional 
machine  is  used,  the  ball  connected  with  the  rubbers  should  be  so 
connected  by  means  of  a  wire.  Connect  the  other  terminal  of  the 
machine  with  the  interior  of  the  metal  can  which  has  previously  been 
placed  upon  the  insulating  stand,  or  upon  a  sheet  of  vulcanite  or  glass. 

(6)  Charge  the  electroscope  by  induction  from  the  vulcanite  rod, 
and  test  the  character  of  its  electrification.  Charge  the  metal  can 
from  the  machine  by  turning  the  plate  of  the  latter  for  a  few  minutes; 
then,  by  means  of  the  vulcanite  rod,  withdraw  the  connecting  wire 
from  the  interior  of  the  former,  leaving  it  charged  and  insulated. 


4 

1- 

•4 

4 

|- 

•4 

4. 

^-4- 

f 

4 

•H      V 

f 

4 

f 

-f 

-l- 

4- 

FIG.  194. 


236  THE  OUTLINES   OF  PHYSICS 

Lower  the  brass  ball  which  takes  the  place  of  the  proof  plane,  being 
more  convenient  than  the  latter  for  this  experiment,  into  the  bottom 
of  the  can,  and  withdraw  it  without  making  contact  with  the  opening. 
Transfer  it  by  means  of  a  glass  handle  to  the  plate  of  the  electro- 
scope, and  note  that  it  brings  no  charge  to  the  latter ;  from  this  we 
conclude  that  the  interior  of  the  can  has  no  electrification. 

(c)  Bring  the  ball  into  contact  with  the  outer  surface  of  the  can, 
and  remove  it  into  the  neighborhood  of  the  electroscope.  The  move- 
ment of  the  leaves  will  indicate  that  the  ball  is  strongly  charged. 

210.  Faraday's  Bag.  —  Faraday,  to  whom  the  preceding 
experiment  is  due,  tested  this  point  in  many  ways.  He 
constructed  a  set  of  buckets,  one  within  another,  and 
showed  that  when  the  interior  of  the  innermost  was 
charged,  the  charge  was  immediately  transferred  by  repul- 
sion to  the  outer  surface  of  the  exterior  vessel.  He  also 
made  use  of  a  conical  bag  woven  of  linen,  which  material  is 

a  conductor  of  electri- 
city. This  is  mounted 
upon  an  insulated  hoop, 
as  shown  in  Fig.  195. 
By  means  of  a  silk  thread 
attached  at  the  apex  of 
the  cone,  this  bag  can  be 
turned  inside  out  with- 
out bringing  it  into  con- 
tact with  any  conducting  body.  When  charged,  the  outer 
surface  shows  electrification.  The  proof  plane  applied 
to  the  interior  of  the  fabric,  however,  shows  no  charge. 
When  the  bag  is  turned  inside  out,  by  drawing  upon  the 
thread  which  is  attached  from  the  interior,  the  charge  is 
found  to  have  transferred  itself  altogether  to  what  then 
becomes  the  outer  surface,  and  the  surface  previously 
without,  but  which  has  now  become  the  inner  surface  of 
the  bag,  is  discharged.  This  is  an  ingenious  modification 


ELECTRIC  CHARGE   UPON   CONDUCTORS 


237 


of  the  ice-pail  experiment.  A  considerable  degree  of 
dexterity  is  required  to  perform  the  experiment  satisfac- 
torily, chiefly  because  the  proof  plane  is  likely  to  become 
charged  by  friction  against  the  linen  fabric  of  which  the 
bag  is  made. 

That  an  electrostatic  charge  gathers  upon  the  outer 
surface  of  conductors  may  be  also  very  simply  demon- 
strated as  follows :  A  strip  of  sheet 
metal,  about  40  cm.  long  and  10  cm. 
wide,  is  bent  into  the  form  abed,  Fig. 
196.  It  is  mounted  upon  an  insulat- 
ing support,  and  pith  balls  attached  to 
short  silk  fibers  are  fastened,  two  to 
the  outside  and  two  to  the  inner  sur- 
face, as  shown  in  the  figure.  When 
this  little  apparatus  is  electrified,  the 
two  outer  pith  balls  become  charged 
by  contact  with  the  surface  and  are 
strongly  repelled ;  those  which  are 
attached  to  the  inner  surface  of  the 
bent  sheet  of  metal  remain  neutral.1 


FIG.  196. 


211.  Quantity  of  Electricity.  —  An  electrostatic  charge 
being  the  result  of  the  expenditure  of  energy,  we  may 
use  the  words  quantity  of  electricity  in  the  same  way  in 
which  we  used  them  in  the  subject  of  Heat.  (See  Arts. 
142  and  146.)  The  unit  by  means  of  which,  or  in  terms 
of  which,  electrical  quantity  is  measured,  is  defined  in  the 
following  manner: 

1  A  tinned  can  of  rectangular  section,  such  as  is  commonly  used  for 
packing  mustard,  spices,  etc.,  may  be  utilized  for  this  experiment.  If  the 
effect  is  to  be  shown  to  a  large  class,  the  bottom  should  be  removed  from 
the  can  as  well  as  the  cover,  so  that  the  apparatus  may  be  placed  in  the 
field  of  the  lantern  for  projection. 


238  THE  OUTLINES   OF  PHYSICS 

The  unit  is  that  quantity  which  at  a  unit's  distance  from 
an  equal  quantity  repels  it  with  unit  force.  The  unit  of 
distance  in  this  definition  is  one  centimeter,  and  the  unit 
of  force  is  one  dyne.  The  space  between  the  charged 
bodies  in  this  definition  is  supposed  to  be  filled  with  air  at 
ordinary  pressure. 

212.  Intensity  of  Charge.  —  When  a  charge  representing 
a  definite   amount  of    electrical  energy  is  imparted  to  a 
body,  it  becomes  distributed  over  the  entire  surface  of  the 
latter.     The  intensity  of  the  effects  produced  will  depend 
upon  the  area  of  that  surface.     If  the  surface  be  small, 
there  will  be  indications  of  a  high  degree  of   electrifica- 
tion upon  it ;  if  the  surface  be  very  large  the  same  quan- 
tity of   electricity  will  not  produce  manifestations  of  so 
high  a  degree  of  electrification  at  any  given  point.     The 
case  is  analogous  to  that  of  heat.     If  a  given  quantity  of 
heat  energy  be  imparted  to  a  small  amount  of  water,  the 
result  will  be  a  great  rise  of   temperature ;   if  the  same 
quantity  be  imparted  to  a  very  large  body  of  water,  the 
rise  of  temperature  will  be  slight.     The  amount  of  energy 
in  the  two  cases  is  the  same.     It  is  represented  by  the 
quantity  of  water  multiplied  by  the  rise  of  temperature 
which  it  undergoes.      The   corresponding  relation  is  ex- 
pressed in  electrostatics  by  means  of  the  words  intensity 
of  charge,  or  sometimes  by  the  words  density  of  charge. 
That   the    intensity  of   electrification,  or   in   other  words 
the    density   of   charge,  depends   upon   the   surface   over 
which  it  is  distributed,  may  be  shown  by  the   following 
experiment : 

213.  EXPERIMENT   65.  —  Diminution  of  Density  of  Charge  with 
Increase  of  Charged  Surface. 

Apparatus : 

A  sheet  of  tin  foil,  mounted  as  shown  in  Fig.  197.     The  figure 


ELECTRIC  CHARGE   UPON  CONDUCTORS 


239 


shows  an  ordinary  spring  curtain  roller,  over  which  a  piece  of  glass 

tubing,  about  30  cm.  long,  has    i 

been  slipped.  The  tube  is  ce-  U| 
mented  to  the  roller  with  seal- 
ing wax  or  with  beeswax-rosin 
cement.  One  end  of  a  sheet 
of  tin  foil  is  fastened  to  the 
glass  tube  by  means  of  shellac. 
When  dry  the  remainder  of 
the  sheet  is  rolled  around  the 
tube,  and  the  roller  is  mounted 
in  the  usual  manner,  so  that 
the  sheet  of  foil  may  be  rolled 
and  unrolled  like  a  curtain. 

A  silk  thread  attached  to  the  middle  of  a  light  rod  or  strip,  which 
is  fastened  along  the  free  end  of  the  sheet  of  foil,  serves  as  a  handle. 
By  drawing  upon  the  silk  thread  carefully,  the  tin  foil  may  be  unrolled 
like  a  window  shade  from  its  roller.  When  released  it  will  be  rolled 
up  again  by  the  action  of  the  springs. 

Procedure : 

(a)  Mount  the  proof  plane  above  the  plate  of  the  electroscope,  at 
the  distance  of  about  five  centimeters.  Attach  a  fine  wire  to  the 
proof  plane,  and  carry  the  same  to  the  foil,  to  the  free  end  of  which 
it  may  be  fastened  by  means  of  a  bit  of  gummed  paper  (Fig.  198). 


FIG.  197. 


FIG.  198. 


(&)  The  foil  being  rolled  up,  electrify  it  gradually  until  the  leaves 
of  the  electroscope  show  marked  divergence.  By  means  of  the  silk 
thread  unroll  the  foil  carefully  and  watch  the  gold  leaves.  As  the 
outer  surface  of  the  foil  increases  in  area  in  the  process  of  being 


240  THE  OUTLINES   OF  PHYSICS 

unrolled,  the  charge  is  compelled  to  distribute  itself  over  greater  and 
greater  areas,  and  it  diminishes  in  density.  This  change  is  indicated 
by  the  gradual  coming  together  of  the  leaves  of  the  electroscope. 
Roll  up  the  foil  again  and  note  that  this  change  was  not  due  to  loss 
of  charge.  The  leaves  will  be  seen  to  dilate  nearly  to  their  former 
position.  Gold  leaves,  attached  directly  to  the  curtain,  will  indicate 
the  change  in  the  density  of  charge  in  the  same  manner  as  the  electro- 
scope. 

214.  Distribution  of  Charge  upon  the  Surface  of  Conductors. 
—  An  insulated  conductor,  when  charged,  does  not  as- 
sume the  same  intensity  of  electrification  at  all  points 
upon  its  surface  unless  it  be  spherical  in  form.  The 
density  of  charge  at  each  point  depends,  in  fact,  upon  the 
curvature  of  the  surface  at  that  point.1 

The  relationship  between  the  electrification  upon  the 
surface  of  the  conductor  and  the  curvature  of  that  sur- 
face, may  be  stated  by  saying  that  the  density  of  charge 
increases  as  the  radius  of  curvature  diminishes.  This 
statement  may  be  verified  by  testing  the  electrification  of 
charged  bodies  of  different  forms. 

CASE  1.  An  ovoid  conductor.  If  an  insulated  con- 
ductor, ovoid  in  form,  be  charged,  and  the  density  of  charge 
at  different  portions  of  its  surface  be 
tested  by  means  of  the  brass  ball  de- 
scribed in  Experiment  64  and  the 
electroscope,  it  is  found  that  the  great- 
est charge  can  be  obtained  by  bringing 
the  ball  into  contact  with  the  more 

1  The  curvature  of  a  surface  is  expressed  by  means  of  what  is  called 
the  radius  of  curvature.  Whatever  form  the  surface  may  have,  we  may 
consider  the  portion  of  it  which  immediately  surrounds  any  given  point 
as  part  of  a  sphere,  provided  we  select  a  sufficiently  small  portion.  The 
length  of  the  radius  which  this  sphere  would  have  is  the  radius  of  curva- 
ture of  the  surface  at  the  point  in  question. 


ELECTRIC  CHARGE  UPON  CONDUCTORS  241 

pointed  end  of  the  conductor.  We  may  indicate  the 
distribution  of  charge  upon  the  surface  of  the  conductor 
by  drawing  a  dotted  line  around  the  conductor,  as  in 
Fig.  199,  the  distance  of  this  line  from  the  surface  indi- 
cating the  intensity  of  the  electrification,  or  the  density 
of  charge. 

CASE  2.  A  disk.  In  this  case  the  radius  of  curvature 
becomes  very  small  at  the  edge  of  the  disk,  and  it  is  here 
that  the  charge  is  chiefly  gathered. 
The  point  may  be  verified  by  bring- 
ing  the  ball  successively  into  con-  FJQ  200 

tact  with  the  edge  of  the  disk  and 

with  a  point  upon  its  plane  surface.  Figure  200  gives  a 
diagram  of  the  distribution. 

CASE  3.  A  cup-shaped  conductor.  Here  the  maximum 
effect  will  be  obtained  at  the  lip  of  the  cup ;  in  the  inte- 
rior scarcely  any  indication  of  the  electrification  can  be 
found.  Upon  the  convex  outer  surface  the  presence  of 
charge  may  be  discovered,  but  the  density  is  less  than  at 
the  lip. 

CASE  4.  A  conductor  carrying  a  point.  In  this  case 
the  charge  will  be  gathered  altogether  at  the  point.  If 
the  point  were  a  perfect  one,  and  so  that  the  radius  of 
curvature  were  reduced  to  zero,  the  density  of  charge 
would  be  relatively  infinitely  great  as  compared  with  that 
on  other  portions  of  the  surface.  Even  with  such  a  point 
as  can  be  actually  produced,  the  radius  of  curvature  is  so 
very  small  that  the  charge  is  almost  entirely  centered  at 
the  point. 

215.  Action  of  Points.  —  A  high  degree  of  electrification 
in  the  neighborhood  of  a  point  upon  any  charged  body 
leads  to  certain  interesting  phenomena.  The  particles  of 


242  THE  OUTLINES  OF  PHYSICS 

air  in  immediate  proximity  to  such  a  point  are  strongly 
attracted.  When  they  come  into  contact  with  the  sur- 
face of  the  charged  body  they  are  electrified  and  repelled. 
Others  take  their  places  and  are  repelled  in  their  turn. 
The  result  is  the  establishment  of  a  convection  current, 
similar  to  that  which  has  been  described  in  Chapter  XX 
(Art.  180).  The  direction  taken,  by  these  currents  is 
shown  in  Fig.  201.  The  existence  of  this  convection 
^—  — \  current  may  be  shown  by 

==<\ JP~*~        mounting    a    point   upon 

any  convenient  conduct- 
ing body.  The  latter  is 
to  be  placed  upon  an  in- 
sulating plate  and  con- 


FlG-  20L  nected  by  means  of  a  wire 

with  the  terminals  of  the  Toepler-Holtz  machine.  The 
flame  of  a  lighted  candle  held  near  the  point  will  be 
strongly  blown  by  the  draft  of  air.  (See  Fig.  201.)  The 

reaction  of  this  convec- 
tion current  takes  the 
form  of  a  backward  thrust 
upon  the  point,  and  if 
the  latter  be  mounted  in 
such  a  manner  that  it  is 
free  to  move,  it  will  be 
driven  in  the  opposite 
direction  from  that  in 
which  the  current  flows. 
This  phenomenon  is  illus- 
trated by  means  of  the 

apparatus  known  as  the  electrical  tourniquet  (Fig.  202). 
This  consists  of  two  wires  at  right  angles  to  one  another, 
the  points  of  which  are  bent  as  shown  in  the  figure.  They 


ELECTRIC   CHARGE   UPON  CONDUCTORS'         243 

are  mounted  upon  a  jeweled  bearing  at  their  common 
center.  When  the  tourniquet  is  charged  from  an  electrical 
machine,  it  revolves  in  the  direction  indicated  by  the 
arrow. 

216.  The  Distribution  of  an  Induced  Charge.  —  The  dis- 
tribution of  charge  upon  bodies,  discussed  in  the  previous 
article,  is  that  which  exists  when  the  charged  body  is  not 
in  the  neighborhood  of  another  electrified  body.  In  the 
latter  case,  the  forces  between  the  positive  and  negative 
charges  modify  the  character  of  the  distribution.  Imagine, 
for  example,  a  small  metal  sphere  which  has  not  been  elec- 
trified. The  density  of  its  charge  is  everywhere  zero.  If 
this  be  brought  into  the  neighborhood  of  a  large  con- 
ductor, positively  charged,  such  as  the  prime  conductor  of 
an  electrical  machine,  it  causes  a  charge  by  induction,  as 
already  described  (Art.  199).  The  portions  of  its  surface 
nearest  the  positively  charged  conductor  will  become  nega- 
tively electrified,  owing  to 

the  attractive  force  between 

'' 
unlike    charges,    while    the  \\{ 

more  remote  parts  of  the  sur-      x\V./x 
face  will  become   positively 
charged  through  the  action 
of  the  forces  of  repulsion  be- 
tween similar  charges. 

The  distribution  will  then 

he  of  the  kind  indicated  in  FlG>  203. 

Fig.  203. 

To  verify  this  statement,  bring  a  small  proof  plane  or 
insulated  brass  ball  into  contact  successively  with  the  posi- 
tive and  negative  portions  of  the  sphere,  and  test  the 
charge  imparted  to  it  by  means  of  the  electroscope.  In 


244  THE  OUTLINES   OF  PHYSICS 

case  the  sphere  were  already  charged  before  being  brought 
into  the  neighborhood  of  the  conductor  of  the  machine,  a 
modification  of  the  distribution  of  the  charge  upon  its  sur- 
face would  likewise  take  place. 

Imagine  the  initial  charge  to  be  positive.  So  long  as 
the  charged  sphere  remains  by  itself  uninfluenced  by 
neighboring  bodies,  the  distribution  of  charge  upon  its 
surface  will  be  uniform.  When  it  is  brought  into  the 
field  of  influence  of  the  charged  conductor,  however, 
the  same  attractive  and  repellent  forces  which  charge 
it  by  induction  in  the  previous  example  will  be  found 
active.  The  positive  charge  upon  the  sphere  will  be 
driven  to  the  most  remote  portions  of  the  surface  by 
the  action  of  repulsion  between  it  and  the  positively 
charged  conductor  of  the  machine.  The  distribution  of 
the  charge  will  therefore  be  a  variable  one  with  a  maxi- 
mum of  density  at  that  point  of  the  surface  which  is 
furthest  away  from  the  conductor  of  the  machine,  and  a 
minimum  at  the  nearest  point  upon  the  surface  of  the 
sphere.  If  the  positive  charge  be  small  as  compared  with 
that  upon  the  conductor  of  the  machine,  it  may  easily 
happen  that  the  surface  of  the  small  sphere  nearest  the 
conductor  will  become  negatively  charged. 

A  similar  case  is  frequently  observed  in  the  use  of  the 
electroscope.  If  the  instrument  be  given  a  slight  positive 
charge  and  a  strongly  charged  vulcanite  rod  be  brought 
near,  the  leaves  are  drawn  together,  and  as  the  charged 
rod  approaches  are  repelled  again.  This  second  repulsion 
is  due  to  a  residual  negative  charge  which  is  no  longer 
neutralized  by  positive  electrification. 


CONDENSERS 


245 


CHAPTER   XXIV 

CONDENSERS 

217.  The  Condenser.  —  When  two  conducting   surfaces 
are  brought  near  together,  and  one  is  charged,  the  other 
becomes  charged  by  induction.     The  process  of  charging 
may  be  carried  on  as  long  as  the  intervening  material  is 
capable  of   resisting   the   attractive   forces  which   are   in 
action,  and  which   are   trying   to   bring  the  two  charges 
together.     Such  an  arrangement  is  called  a  condenser.     It 
may  be  regarded  as  a  device  for  storing  electrical  energy, 
since,  when   the   two   charges   are   allowed  to  unite,  an 
amount  of  energy  which  is  equivalent  to  the  sum  of  all 
the  energy  expended  in  charging  the  condenser  is  obtained. 

218.  The  Leyden  Jar.  —  One  of  the  best-known  forms 
of  condenser  is  the  Leyden  jar  (Fig.  204).     It  consists  of 
a  wide-mouthed  bottle  of  thin  glass,  the  inner 

and  outer  surface  of  which  are  coated  with  tin 
foil  from  the  bottom  upwards  for  about  two 
thirds  of  its  height.  The  inner  coating  is  con- 
nected, by  means  of  a  chain  or  wire,  with  a  rod 
which  is  inserted  through  the  cover  of  the  jar. 
This  rod  ends  above  in  a  ball  or  plate.  The 
two  layers  of  tin  foil,  together  with  the  inter- 
vening layer  of  glass,  form  a  condenser.  They 
are  commonly  spoken  of  as  the  inner  coating 

•  FIG    204 

and  the  outer  coating.     The  object  of  the  rod 

and  ball  is  simply  to  give  convenient  connection  between 


246  THE   OUTLINES   OF  PHYSICS 

the  inner  coating  and  the  outer  air.  The  apparatus 
derives  its  name  from  the  city  of  Leyden  in  Holland, 
where  it  is  said  to  have  been  discovered  by  a  student  of 
electricity  named  Cuneus,  who  was  experimenting  on  the 
charging  of  a  glass  of  water.  He  held  the  glass  in  the 
palm  of  his  hand,  and  connected  the  liquid  with  the  con- 
ductor of  an  electrical  machine.  Upon  removing  the 
liquid  from  contact  with  the  machine,  and  touching  it 
with  the  other  hand  to  see  whether  it  was  charged,  he 
received  a  severe  shock.  The  water  formed  the  inner 
coat  of  the  condenser,  and  the  hand  in  which  the  glass 
was  held,  the  outer  coat.  This  stored  a  considerable 
amount  of  electrical  energy  during  the  time  that  the 
water  was  in  connection  with  the  machine,  all  of  which 
was  instantly  released  when  Cuneus  made  contact  between 
his  other  hand  and  the  liquid. 

219.  Specific  Inductive  Capacity.  —  The  capacity  of  a 
condenser  increases  as  its  surface  increases,  and  the  dis- 
tance between  its  plates  is  diminished.  The  capacity  also 
depends  upon  the  character  of  the  intervening  medium. 

The  word  capacity  is  used  in  the  above  statements  with 
reference  to  the  quantity  of  electricity  which  the  condenser 
is  capable  of  storing  under  given  conditions.  The  quality 
of  the  intervening  medium  with  reference  to  the  extent 
to  which  induction  takes  place  through  it,  is  termed  its 
specific  inductive  capacity.  The  specific  inductive  capacity 
of  air  is  considered  to  be  equal  to  unity,  and  the  specific 
inductive  capacities  of  other  substances  are  expressed  in 
terms  of  this.  Thus,  paraffin  has  a  specific  inductive 
capacity  of  1-99,  sulphur  of  2*58,  shellac  of  2-74,  and  glass 
of  3-25. 


CONDENSERS  247 

220.    EXPERIMENT  66.  —  The  Leyden  Jar. 

Apparatus : 

(1)  The  Leyden  jar. 

(2)  An  electrical  machine  (either  a  Toepler-Holtz  or  a  frictional 
machine  will  do). 

(3)  The  electrophorus. 

(4)  A  discharger.     (The  discharger  consists  of  a  jointed  rod  tipped 
with  brass  balls  [Fig.  205].     It   is  mounted   upon   a 

handle  of  glass.  By  means  of  this  instrument,  the 
balls  of  which  are  adjustable  as  to  their  distance  apart, 
the  outer  coating  and  the  ball  of  the  Leyden  jar  can  be 
readily  connected  without  danger  of  sending  the  dis- 
charge through  the  hand  or  body  of  the  operator.) 

Procedure : 

(a)  Charge  the  electrical  machine,  using  the  electro- 
phorus to  set  it  into  action  if  necessary. 

(V)  Place  the  vulcanite  plate  of  the  electrophorus  FlG  205. 
near  the  machine  and  upon  it  a  Leyden  jar,  connecting 
the  knob  of  the  jar  with  the  conductor  of  the  machine,  and  the  other 
terminal  of  the  machine  with  the  ground  (i.e.  with  the  nearest  gas  or 
water  pipe)  ;  these  connections  should  be  made  by  means  of  copper 
wire,  or  with  chains.  Connect  also  the  outer  coating  of  the  Leyden 
jar  with  the  ground. 

(c)  Turn  the  plate  of  the  machine  for  about  one  minute,  and  then 
bring  one  ball  of  the  discharger  to  the  outer  coating,  and  the  other  to 
the  knob  of  the  jar.  If  the  machine  has  been  acting  properly,  there 
will  be  a  heavy  spark  which  indicates  that  a  considerable  amount  of 
energy  has  been  stored  in  the  charging  of  the  jar. 

(df)  Disconnect  the  outer  coating  from  the  earth,  leaving  it  care- 
fully insulated  by  the  vulcanite  plate  upon  which  the  jar  stands. 
Put  the  machine  into  motion  as  before,  for  about  the  same  length  of 
time,  then  discharge  the  jar  as  in  operation  (c),  and  compare  the 
character  of  the  discharge  with  that  previously  noted.  It  will  be 
seen  that  the  spark  is  now  very  insignificant  indeed.  The  reason  for 
this  condition  is  that  in  the  latter  experiment  no  opportunity  was 
given  for  the  repelled  charge  upon  the  outer  coating  to  escape.  How- 
ever strongly,  therefore,  the  outer  coating  may  have  been  charged  by 
induction,  this  charge  would  be  temporary.  Under  these  circum- 
stances no  considerable  storage  of  electrical  energy  takes  place. 


248 


THE  OUTLINES   OF  PHYSICS 


FIG.  206. 


(e)  Arrange  the  apparatus  as  shown  in  Fig.  206.  The  wire  con- 
necting the  machine  with  the  inner  coating  is  to  be  supported  upon 

a  glass  rod,  and  its  end  is  not  to 
make  contact  with  the  knob  of  the 
jar.  The  intervening  air  space 
should  be  about  1  cm.  The  wire 
between  the  outer  coating  and  the 
earth  is  to  be  removed  from  the 
outer  coating  by  about  the  same  dis- 
tance. This  arrangement  perfected, 
repeat  operation  (c),  and  note  that 
whenever  the  spark  passes  between 
the  machine  and  the  knob  of  the  jar, 
a  similar  spark  leaps  across  the  air 
space  between  the  outer  coating  and 
the  wire  which  leads  to  the  earth. 
Under  these  conditions  the  jar  be- 
comes strongly  charged,  as  may  be  shown  by  the  use  of  the  dis- 
charger. 

(/)  The  condenser  cannot  be  discharged  by  contact  with  one 
coating  at  a  time.  To  test  this  point  charge  the  jar  as  described  in 
operation  (c)  ;  then  remove  the  wire  which  connects  the  outer  coating 
with  the  earth,  thus  leaving  the  jar  insulated.  Place  one  hand  behind 
the  back,  and  with  the  other  touch  the  knob  of  the  jar.  Note  that 
while  a  feeble  spark  passes  between  the  hand  and  the  jar,  the  dis- 
charge is  not  in  any  way  comparable  with  that  which  occurs  when 
the  two  coatings  are  connected  together.  Let  go  the  knob  and  then 
touch  the  insulated  outer  coating  with  the  hand.  Another  slight 
spark  passes  between  the  finger  and  the  coating.  The  jar,  however, 
is  still  strongly  charged,  as  may  be  shown  by  the  use  of  the  discharger. 
The  reason  for  putting  one  hand  behind  the  back  in  performing  this 
experiment  is  that  while  the  discharge  of  a  single  Leyden  jar  through 
the  body  is  not  in  any  way  dangerous,  although  rather  unpleasant, 
this  is  the  method  which  insures  safety  in  experimenting  with  charged 
condensers  and  other  electrical  apparatus.  In  some  experiments  it 
would  be  a  more  serious  matter  to  receive  the  discharge  through  the 
body.  The  habit  of  always  working  with  one  hand  behind  the  back 
is  easily  acquired,  and  it  secures  immunity  from  many  unpleasant 
experiences. 


CONDENSERS 


249 


221.  EXPERIMENT  67.  —  The  Capacity  of  a  Condenser  increases 
with  the  Area  of  its  Coatings. 

Apparatus  : 

(1)  Four  Leyden  jars. 

(2)  A  Toepler-Holtz  machine. 

Procedure  : 

(a)  Remove  the  small  Leyden  jars  which  are  attached  to  the 
machine. 

(&)  Get  the  machine  into  action  and  drive  it  without  the  jars  for 
half  a  minute  at,  as  nearly  as  possible,  a  uniform  speed,  noting  the 
rapidity  with  which  sparks  pass  between  the  terminals  of  the  machine, 
and  noting  likewise  the  appearance  of  the  sparks.  The  terminals 
should  be  adjusted  to  a  distance  of  1  cm.  by  means  of  a  piece  of 
wood  of  that  thickness,  used  as  a  gauge. 


T^^ 
\ 
\ 
\ 
\ 
•v^_ 

o 

/ 
/ 
/ 
/ 
/ 

^^ 

0 

/* 

s 

? 

y 

FIG.  207. 


FIG.  208. 


(c)  Lay  a  pane  of  glass  in  front  of  the  machine  and  place  one  of 
the  four  Leyden  jars  upon  the  glass.  Connect  the  knob  of  the  jar  to 
one  terminal  of  the  machine,  and  the  other  terminal  to  the  outer 
coating  of  the  jar,  as  shown  in  Fig.  207.  Drive  the  machine  as  before 
and  note : 

(1)  That  the  sparks  pass  much  less  frequently  and  that  each  is 
much  heavier  than  before,  i.e.  that  it  is  louder  and  gives  more  light. 
Estimate  approximately  the  number  of  turns  of  the  handle  of  the 
machine  to  each  spark. 


250 


THE  OUTLINES   OF  PHYSICS 


(d)  Place  an  additional  jar  upon  the  glass,  the  outer  coatings  in 
contact.     Connect  the  knobs  by  means  of  a  wire,  as  in  Fig.  208,  and 
repeat  observation  (c).     Note  that  sparks  occur  at  even  greater  inter- 
vals, and  that  each  one  represents  a  greater  amount  of  energy  than 
before.    Estimate  again  the  relation  between  sparking  intervals  and 
revolutions  of  the  handle  of  the. machine. 

(e)  Repeat,  with  three  and  finally  with  four  jars. 

The  Leyden  jars,  whatever  their  number,  when  connected  as 
above,  form  a  single  condenser,  the  surface  of  which  is  proportional 
to  the  number  of  jars.  The  increasing  length  of  time  necessary 
to  produce  an  intensity  of  charge  sufficient  to  give  a  spark  affords 
a  direct  indication  of  the  increased  capacity  as  each  jar  is  added. 

It  does  not  afford  an  exact  measure  of  the  capacity,  because  of  the 
irregular  manner  in  which  Toepler-Holtz  machines  work  even  when 
driven  at  constant  speed. 


—  Bound  and  Free  Charges. 


222.   EXPERIMENT 

Apparatus : 

(1)  The  gold-leaf  electroscope. 

(2)  The  electrophorus. 

(3)  A  sheet  of  plate  glass  about  20  cm.  square. 


FIG.  209. 

(4)  A  condenser  of  the  form  shown  in  Fig.  209.  This  instrument 
is  known  as  an  air  condenser.  It  consists  of  two  metallic  disks, 
mounted  vertically  and  coaxially  upon  insulating  supports.  One  or 
both  of  them  should  have  freedom  of  motion  in  the  direction  of  their 
common  axis. 


CONDENSERS 


251 


Procedure  : 

(a)   Remove  one  plate  of  the  air  condenser  to  a  considerable  dis- 
tance from  its  neighbor,  and  attach  the  other  plate  to  the  disk  of  the 


FIG.  210. 

electroscope,  as  shown  in  Fig. ,,210,  by  means  of  a  fine  wire.  Charge 
the  attached  plate  until  the  leaves  of  the  electroscope  show  a  dilation 
of  nearly  90°. 

(5)  Move  up  the  free  plate  of  the  condenser  until  the  distance 
between  it  and  the  attached  plate  is  equal  to  the  thickness  of  the 
glass.  (One  corner  of  the  sheet  of  glass  may  be  used  as  a  gauge, 
provided  care  has  been  taken  not 
to  electrify  by  cleaning  it  with  paper, 
silk,  or  wool.)  Note  that  the  leaves 
of  the  electroscope  come  together 
upon  the  approach  of  the  plates. 
The  charged  system  has  not  been 
discharged,  but  the  charge  upon  it 
is  said  to  be  "bound"  by  the  con- 
denser action  between  the  plates. 

(c)  Withdraw  the  free  plate  and 
note  the  gradual  freeing  of  the 
charge,  as  indicated  by  the  dilation 
of  the  leaves  of  the  electroscope. 

(t/)  By  means  of  a  joiner's  clamp 
and  blocks  mount  the  glass  plate  vertically  in  front  of,  and  in  con- 
tact with,  the  attached  plate,  as  in  Fig.  211.  (Care  must  be  taken 
to  handle  the  glass  so  as  not  to  electrify  it.)  Charge  the  attached 


FIG.  211. 


252 


THE   OUTLINES   OF  PHYSICS 


plate  again  to  about  the  same  intensity  as  before.  Move  up  the  free 
plate  until  it  touches  the  glass,  and  note  the  effect  upon  the  electro- 
scope. The  condenser  action  is  much  more  marked  on  account  of  the 
high  specific  inductive  capacity  of  the  glass.  By  removing  the  glass 
without  discharging  the  attached  plate,  it  will  be  found  possible  to 
compare  the  effects  of  glass  and  air  when  used  as  a  dielectric.1  It 
will  be  found  necessary  to  bring  the  plates  of  the  condenser  together 
until  their  distance  is  about  one  third  the  thickness  of  the  glass  plate, 
to  obtain  the  same  action. 

To  have  the  same  capacity  as  an  air  condenser,  therefore,  a  con- 
denser with  glass  as  the  dielectric  will  have  only  one  third  the  surface, 
provided  the  coatings  are  the  same  distance  apart  in  the  two  cases. 
Glass,  on  account  of  this  property,  is  one  of  the  best  materials  with 
which  to  insulate  condenser  plates ;  where  large  capacity  is  desired, 
however,  this  may  be  obtained  more  compactly  by  bringing  plates  of 
large  surface  very  close  together  with  mica,  or  paraffined  paper,  as  a 
dielectric. 

This  experiment  may  be  performed  in  a  simpler  manner  by  using 
the  metal  disk  of  the  electroscope,  and  that  of  the 
electrophorus,  as  the  two  plates  of  the  air  condenser. 

Bring  the  latter  down  over  the  disk  of  the  electro- 
scope as  in  Fig.  212.  Touch  the  upper  disk  to  con- 
nect it  to  earth,  and  note  the  effect  upon  the  gold 
leaves.  Then  place  the  glass  plate  upon  the  disk 
of  the  electroscope,  bring  the  dilation  of  the  leaves 
to  the  same  degree  by  further  charging  with  vulcan- 
ite, and  bring  the  electrophorus  disk  down  upon  the 
glass.  Connect  with  earth,  and  note  the  greatly  in- 
creased condenser  action  due  to  the  presence  of  the 

FIG.  212.         glaSS*     The  exPeriment  in  this  form  frequently  suc- 
ceeds when,  owing  to  the  state  of  the  atmosphere, 
difficulty  is  encountered  in  carrying  it  out  in  the   form  previously 
described. 


223.   The  Quadrant  Electrometer.  —  For  the  experiments 
hitherto  described,  the  gold-leaf  electroscope  is  sufficiently 

1  Dielectric  :  the  name  applied  to  any  material  through  which  electro- 
static induction  takes  place. 


CONDENSERS 


253 


FIG.  213. 


sensitive.  It  is  possible,  however,  to  construct  instru- 
ments of  far  greater  delicacy.  One  of  the  most  useful  of 
these  is  the  quadrant  electrometer.  It  con- 
sists of  a  thin  sheet  of  aluminium,  called 
the  needle  which  is  shown  in  Fig.  213. 
This  is  suspended  by  means  of  two  par- 
allel fibers  of  unspun  silk  attached  to  a 
platinum  wire  which  passes  through  the  center  of  the 
needle.  To  the  other  end  of  this  wire,  which  extends 
below  the  needle,  is  attached  a  tiny  vane  of  platinum. 
(See  Fig.  214.)  The  needle  hangs  in  the  middle  of  a 
flat,  cylindrical  box  of  brass  which  is  cut  diametrically 
through  in  two  directions,  and  is  thus  divided  into  quad- 
rants (Fig.  215).  These  quadrants  are  slightly  separated 


FIG.  215. 


FIG.  21G. 


from  one  another,  and  are  mounted  upon  glass  posts  which 
serve  as  insulators.  A  glass  jar  below  has  an  outer  coating 
of  foil  like  a  Leyden  jar.  Within,  it  is  partly  filled  with 


254 


THE  OUTLINES   OF  PHYSICS 


strong  sulphuric  acid.  This  is  placed  at  such  a  height 
that  the  vane  v  attached  to  the  needle  dips  into  the  acid. 
Figure  216  shows  the  arrangement  of  a  simple  form  of  a 
quadrant  electrometer. 

A  small  mirror,  m  (Fig.  214),  is  attached  to  the  plati- 
num wire  above  the  needle.  By  means  of  the  direction  in 
which  it  reflects  a  beam  of  light  thrown  upon  it,  every 
movement  of  the  needle  is  indicated. 

To  use  the  electrometer,  the  acid  within  the  jar  is 
charged  by  means  of  the  electrophorus.  The  charge  is 
shared  by  the  needle,  since  the  latter  is  in  contact  with  the 
acid  through  the  platinum  wire  and  vane.  The  position 
of  the  needle  within  the  box  is  shown  by  the  dotted  line 
in  Fig.  215.  If  two  opposite  quadrants  as  aa,  or  bb,  be 
given  a  small  charge,  the  needle  will  turn  either  towards 


FIG.  217. 


FIG.  218. 


them,  in  case  the  charge  is  unlike  that  of  the  needle 
(Fig.  217),  or  away  from  them,  if  the  charges  be  similar 
(Fig.  218).  With  this  arrangement,  exceedingly  small 
degrees  of  electrification  can  be  detected  and  measured. 


THE  ELECTRIC  SPARK  255 


CHAPTER   XXV 
THE  ELECTRIC  SPARK 

224.  The  Disruptive  Discharge.  —  When  two  neighboring 
conductors,  such  as  the  terminals  of  an  electrical  machine, 
are  oppositely  electrified,  there  is  attraction  between  them 
which  increases  as  the  intensity  of  electrification  increases. 
The  intervening  medium  resists  this  pull  between  the 
charged  bodies,  and,  in  so  doing,  is  strained  as  a  spring 
is  strained  when  subjected  to  forces. 

In  the  case  of  the  dielectric,  as  in  that  of  a  spring, 
energy  is  stored  in  the  production  of  this  strained  condi- 
tion, to  be  released  when  the  strained  medium  returns  to 
its  normal  state. 

If  the  electrification  be  carried  far  enough,  the  dielectric 
is  no  longer  able  to  withstand  the  strain.  An  electric 
spark  then  passes  between  the  conductors,  and  they  are 
discharged.  Such  a  discharge  is  called  the  disruptive  dis- 
charge because  it  follows  a  breaking  down  of  the  medium 
under  excessive  strain. 

The  discharge  manifests  itself  in  two  ways : 

(1)  By  means  of  a  flash.     The  path  along  which  the 
discharge  takes  place  is  heated  intensely, -and  the  medium, 
whether  a  gas,  a  liquid,  or  a  solid,  is  momentarily  rendered 
brilliantly  incandescent.     Nearly  all  the  stored  energy  is 
thus  transformed  into  heat  and  is  dissipated. 

(2)  By  means  of  a  report.      A  certain  portion  of  the 
stored  energy  is  dissipated  in  the  form  of  sound  waves. 


256 


THE   OUTLINES   OF  PHYSICS 


225.  Path  of  the  Spark.  —  The  spark  always  occupies 
the  path  of  least  resistance.  In  a  perfectly  homogeneous 
medium,  this  path  is  a  straight  line,  but  in  air,  the  spark 
usually  follows  a  crooked  path,  as  shown  in  Fig.  219, 


Fro.  219. 

which  is  from  a  photograph  of  a  spark  between  the  termi- 
nals of  a  Holtz  machine.  The  irregularity  of  such  paths 
is  due  to  the  presence  of  dust  in  the  air. 

226.  Energy  of  the  Spark.  —  The  energy  set  free  when 
disruptive  discharge  occurs  increases  with  the  length  of 
the  spark  and  is  directly  proportional  to  the  capacity  of 
the  discharged  conductors. 

To  illustrate  this  relation,  drive  a  Toepler-Holtz  machine 
at  as  nearly  uniform  rate  as  possible.  Adjust  the  distance 
between  the  terminals  until  the  sparks  follow  one  another 
at  intervals  of  about  one  second.  Note  the  character 
of  the  spark  as  regards  length  of  path  and  apparent 
^ — -^  thickness.  Attach  two  additional 

/  \  Leyden  jars  to  the  machine,  as 

shown  in  Fig.  220.  The  outer 
coating  of  each  is  to  be  in 
metallic  contact  with  the  fixed 
jar  upon  the  same  side  of  the 
machine,  the  inner  coatings  con- 
nected with  the  respective  ter- 
minals. Now  drive  the  machine  at  the  same  speed  and 


FIG.  220. 


THE  ELECTRIC  SPARK 


257 


readjust  the  knobs  until  the  sparks  occur  with  the  same 
frequency.     It  will  be  found : 

(1)  that  the  length  of  spark  is  less  than  before ; 

(2)  that  the  spark  is  thicker. 

Since  the  machine  is  driven  at  the  same  speed  in  the 
two  trials,  we  may  assume,  for  the  purpose  of  this  ex- 
periment, that  it  produces  electrical  energy  at  the  same 
rate;  and  since  the  sparks  occur  with  equal  rapidity  in 
the  two  cases,  they  represent  the  same  amounts  of  energy 
converted  into  heat.  The  two  sparks  are  equivalent,  but 
not  identical.  We  may  distribute  the  energy  over  a  long 
path,  producing  a  long,  thread-like  spark,  or  concentrate 
it  by  increasing  the  capacity  of  our  storage  reservoirs  and 
by  bringing  the  terminals  of  the  machines  nearer  together. 

227.  Influence  of  Pressure  upon  the  Spark.  —  The  form 
of  spark  described  in  the  foregoing  articles  occurs  in  air  at 
ordinary  pressures.  If  we  greatly  reduce 
the  pressure,  the  discharge  undergoes  re- 
markable changes.  These  may  be  conven- 
iently observed  by  means  of  the  apparatus 
shown  in  Fig.  221.  This  is  a  glass  re- 
ceiver, fitted  with  brass  caps.  Through 
this  are  introduced  brass  terminals,  one  of 
which  is  adjustable  ;  also  a  tube  with  a 
stopcock,  which  connects  the  receiver  with 
the  air  pump.  If  the  upper  terminal  be 
pushed  down  until  the  air  gap  is  reduced 
to  a  few  centimeters,  and  the  terminals 
be  connected  with  those  of  an  electrical 
machine  by  means  of  wires,  sparks  of  the 
character  usual  in  air  will  be  obtained. 


FIG.  221. 


Upon  exhausting  the  receiver  by  means  of  the  air  pump, 


258  THE  OUTLINES   OF  PHYSICS 

the  sparks  gradually  change  their  appearance.  They  pass 
more  frequently  and  are  less  intense,  showing  that  the 
dielectric  strength  of  the  air  diminishes  with  the  falling 
pressure.  The  path  of  the  spark  becomes  ill  defined,  and 
the  layers  of  air  immediately  surrounding  it  begin  to  glow 
with  a  bluish  or  purple  light.  As  the  pressure  decreases, 
this  illuminated  region  extends,  it  becomes  brighter,  while 
the  original  linear  path  gradually  vanishes  from  view. 
When  the  pressure  has  been  reduced  to  a  few  centimeters 
of  mercury,  the  entire  atmosphere  within  the  receiver 
partakes  of  the  purple  glow.  It  will  now  be  found  that 
the  upper  terminal  may  be  withdrawn  to  the  very  top 
of  the  receiver  without  interrupting  the  discharge.  A 
machine  which  is  capable  of  producing  a  spark  a  few  cen- 
timeters long  in  air  at  ordinary  pressure  will  discharge 
through  much  greater  distances  in  rarefied  air.  This 
point  may  be  illustrated  by  means  of  the  following  ex- 
periment : 

228.    EXPERIMENT  69.  —  Equivalent  Spark    Length  of    the  Dis- 
charge in  Vacuo. 
Apparatus  : 

(1)  A  glass  tube  between  0-5  cm.  and  1-0  cm.  in  diameter  and  at 
__._  least  200  cm.  long.1 

(2)  Mercury  (enough  to  fill  the 

b  ^^^  =^s  -^~  closed  tube,  leaving  an  excess  of  at 

least  100  cm.3),  also  a  glass  tumbler. 

— ^ o  (3)  The  Toepler-Holtz  machine. 

FIG.  222.  (4)  A  barometer. 

1  This  tube  is  to  be  drawn  out  at  one  end  in  the  flame  of  a  blast  lamp, 
as  shown  in  Fig.  222,  a,  until  the  bore  in  the  contraction  is  reduced  to 
about  1  mm.  The  tube  is  then  to  be  cut  off  where  the  diameter  is  smallest, 
6,  and  a  piece  of  platinum  wire  3  or  4  cm.  long  is  to  be  inserted.  The  end 
of  the  tube  is  then  sealed  around  the  wire,  c,  and  completely  closed  by 
means  of  the  flame. 


THE  ELECTEIC  SPARK 


259 


Procedure : 

(«)  Fill  the  closed  tube  with  mercury,  close  the  end  with  the  fore- 
finger, then  invert  it  carefully  in  the  tumbler.  The  latter  should 
already  contain  the  excess  of  mercury  to  insure  prompt  immersion  of 
the  open  end.  The  mercury  will  flow  out  until  the  proper  barometric 
height  is  reached,  leaving  a  Torricellian  vacuum  above  the  mercury 
column  more  than  a  meter  in  length. 


FIG.  223. 

(ft)  Support  the  inverted  tube  in  a  vertical  position  and  connect  the 
outer  end  of  the  platinum  terminal  at  the  top  of  the  tube  with  one 
pole  of  the  Toepler-Holtz  machine  by  means  of  a  flexible  wire.  Attach 
a  wire  to  the  other  terminal  of  the  machine  and  dip  the  free  end  into 
the  mercury  within  the  tumbler.  (See  Fig.  223.) 

(c)  Push  the  terminals  of  the  machine  together,  start  the  machine, 
then  very  gradually  draw  the  terminals  apart  again.  Note  that  at 
first  sparks  pass  between  the  knobs.  Before  the  latter  are  any  con- 
siderable distance  apart,  however,  the  discharge  abandons  the  direct 


260  THE  OUTLINES  OF  PHYSICS 

path  between  them  and  passes  between  the  platinum  wire  at  the  top 
of  the  tube  and  the  surface  of  the  mercury  column.  The  tube 
becomes  filled  with  a  whitish  or  bluish  glow.  Push  the  terminals  of 
the  machine  together  until  the  spark  returns  to  the  space  between  the 
knobs.  Measure  the  distance  between  them  in  centimeters.  Draw 
the  knobs  apart  until  the  spark  again  transfers  itself  to  the  tube. 
Measure  the  distance  again.  Repeat  these  alternate  measurements 
five  times.  The  average  of  the  entire  set  may  be  taken  as  the  spark- 
ing distance  in  air,  which  is  equivalent  to  the  discharge  within  the 
tube. 

(rf)  Measure  the  distance  between  the  top  of  the  mercury  column 
and  the  platinum  terminal  within  the  top  of  the  tube.  Express  this 
length  in  terms  of  the  sparking  distance  in  air.  Finally,  measure  the 
height  of  the  mercury  column  in  centimeters  and  compare  it  with 
the  true  barometric  height  for  the  time  and  place.  The  difference 
between  these  heights  will  give  the  pressure,  in  centimeters  of  mer- 
cury, for  which  the  comparison  of  sparking  distances  has  just  been 
made. 

This  experiment  may  be  repeated,  at  different  pressures,  by  letting 
a  bubble  of  air  into  the  vacuum,  repeating  the  measurements  under 
(c)  and  (Y/),  admitting  more  air  from  time  to  time,  until  the  discharge 
can  no  longer  be  driven  through  the  tube. 

229.  Intermittent  Character  of  the  Discharge  in  Vacuo.  — 
The  discharge  through  the  Torricellian  vacuum,  described 
in  Art.  227,  often  appears  to  be  nearly  or  quite  continuous. 
It  is,  however,  as  truly  intermittent  as  the  spark  discharge 
in  air.  This  may  be  shown  by  the  use  of  the  revolving 
mirror  depicted  in  Fig.  224.  It  consists  of  four  square, 
plane  mirrors  mounted  so  as  to  form  the  vertical  sides  of 
a  cube  which  revolves  upon  an  axis  passing  through  the 
centers  of  the  remaining  faces.  When  we  view  the  image 
of  the  tube  through  which  the  discharge  occurs  in  this 
mirror,  the  illuminated  region,  instead  of  being  spread  out 
into  a  continuous  sheet,  is  broken  up  into  a  series  of  par- 
allel, bright  images  when  the  mirror  revolves.  Each  of 
these  appears  just  as  it  would  in  a  stationary  mirror. 


THE  ELECTRIC  SPARK 


261 


FIG.  224. 


Each  is  displaced  from  its  neighbor  by  the  angular  dis- 
tance through  which  the  mirror  has  turned  between  the 
successive  discharges.  The  fact  that 
the  images  in  the  moving  mirror  are 
not  appreciably  broadened  indicates 
that  the  discharge  is  so  brief  in  dura- 
tion that  the  mirror  does  not  turn 
through  a  noticeable  angle  during  the 
life  of  the  spark.  The  same  obser- 
vation may  be  made  upon  the  ordinary 
spark  in  air.  This  breaking  up  of  the 
image  of  the  discharge  may  be  ob- 
served, although  less  conveniently,  by 
viewing  it  in  a  common  hand  mirror, 
and  giving  the  mirror  a  sudden  turn  to  the  right  or  left. 
It  may  even  be  observed  by  turning  the  head  suddenly 
while  looking  at  the  discharge,  provided  the  eyes  be 
allowed  to  follow  the  motion  of  the  head  instead  of 
remaining  fixed  upon  the  tube. 

By  means  of  mirrors  revolving  at  much  higher  speeds, 
it  is  found  that  the  electric  spark  is  not  instantaneous,  but 
has  a  duration  amounting,  in  general,  to  a  few  millionths 
of  a  second. 

230.  Discharge  in  Higher  Vacua.  —  By  means  of  mercu- 
rial pumps,  it  is  possible  to  carry  the  exhaustion  of  a  tube 
or  receiver  much  further  than  in  the  experiments  just 
described. 

When  a  tube  with  two  metallic  terminals  sealed  into 
the  glass  (Fig.  225)  is  thus  exhausted,  we  get,  as  the 

pressure  falls,  a  sue-  C — «^-          ^^ .^&  3 

cession     of     further  FlG-  225- 

modifications  in  the  discharge.      In  such  a  tube,  so  long 


262  THE  OUTLINES   OF  PHYSICS 

as  the  pressure  exceeds  about  0-5  cm.,  the  discharge  pre- 
sents the  appearance  already  described.  A  tube  in  this 
condition  is  termed  a  Greissler1  tube.  When  the  pres- 
sure is  further  reduced,  the  discharge  becomes  laterally 
laminated  and  undergoes  a  succession  of  beautiful  and 
striking  changes.  Finally,  the  discharge  within  the 
tube  becomes  nearly  invisible.  There  now  emanate 
from  the  terminal,  which  is  connected  with  the  nega- 
tive pole  of  the  electrical  machine,  rays  which  travel 
in  straight  lines  through  the  tube.  Wherever  these 
impinge  upon  the  glass,  the  walls  of  the  tube  glow 
with  a  bright  green  phosphorescence.  In  this  condition 
the  surface  of  the  tube  emits,  externally,  invisible  rays 
which  are  known  as  the  Roentgen  rays,  or  as  the  X 
rays.  These  pass  through  many  opaque  substances,  such 
as  aluminium,  hard  rubber,  wood,  flesh,  most  textile  fab- 
rics, etc.,  while  they  are  absorbed  by  some  transparent 
materials,  such  as  glass.  They  affect  the  photographic 
film,  so  that  shadow  photographs  may  be  taken  by  means 
of  them ;  and  they  render  certain  substances,  such  as  cal- 
cium tungstate,  zinc  oxide,  and  many  of  the  double  plati- 
num cyanides,  luminous.  If  a  screen  coated  with  one  of 
these  substances  be  placed  in  the  path  of  the  X  rays,  the 
shadow  of  any  body  interposed  will  be  visible  upon  the 
screen.  This  will  be  the  shadow  of  those  portions  of  the 
body  which  are  opaque  to  the  X  rays,  and  not  of  those 
opaque  to  ordinary  light.  Thus,  if  the  arm  be  interposed, 
the  two  bones  will  be  clearly  visible,  but  the  fleshy  part 
of  the  arm  will  scarcely  cast  any  shadow. 

Photographs  taken  with  the  X  rays  possess  the  same 
peculiarity.     Figure  226  is  a  reproduction  of  such  a  photo- 

1  From  Dr.  Geissler,  of  Bonn. 


THE  ELECTRIC  SPARK 


263 


graph.1  It  shows  the  bones  of  the  human  wrist;  also  a 
bit  of  broken  needle  which  had  become  lodged  in  the 
membrane  surrounding  one  of  the  bones.  The  outline  of 
the  wrist  is  dimly  visible. 


FIG.  226. 
1  From  a  photograph  taken  by  K.  W.  Quick. 


264 


THE  OUTLINES  OF  PHYSICS 


CHAPTER   XXVI 

THE  ELECTRIC   CURRENT 

231.    Electrification  by  Chemical  Action.  —  Thus  far  we 

have  considered  the  electrification  of  bodies  by  friction.  It 
is  also  possible  to  electrify  two  metaLs, 
oppositely,  by  chemical  action.  It  is 
usual  to  speak  of  two  conductors 
thus  electrified  as  possessing  a  differ- 
ence of  potential.1  If  a  piece  of  zinc 
and  a  piece  of  copper,  for  example, 
be  placed  in  a  glass  (Fig.  227)  con- 
taining an  acid,  such  as  dilute  sul- 
phuric acid,  the  copper  will  become 
positively,  and  the  zinc  negatively, 
electrified.  Such  an  arrangement  is 
called  a  voltaic  cell.2  The  source  of 

electrical  energy,  in  this  case,  is  the  chemical  reaction 

between  the  zinc  and  the  acid. 

This   difference    of   potential   is  so  small   that   it   can 

scarcely  be  shown  by  means  of  an  ordinary  electroscope. 

With  the  quadrant  electrometer  described  in  a  previous 

<& 

1  The  term  difference  of  potential  is  frequently  used  in  speaking  of 
the  difference  of  electrical  condition  of  bodies,  however  electrified.     If  a 
positively  and  negative'ly  charged  conductor  be  metallically  connected, 
there  will  be  electric  flow,  and  their  charges  will  unite.     If  a  charged 
body  and  a  neutral  one  are  connected,  there  will  be  electric  flow,  and  the 
former  will  share  its  charge  with  the  latter.    In  all  such  cases,  we  say 
that  there  was  difference  of  potential. 

2  From  the  Italian  physicist,  Volta,  1745-1827. 


^^M^ 
FIG.  227. 


THE  ELECTRIC  CURRENT  265 

article,  a  considerable  deflection  will  be  produced  when 
one  pair  of  quadrants  is  connected  to  the  zinc  and  one  to 
the  copper.  By  getting  together  a  large  number  of  such 
cells,  the  copper  of  each  connected  to  the  zinc  of  the  next, 
we  are  able  to  add  together  their  individual  differences  of 
potential,  and  to  secure  a  battery,  the  difference  of  poten- 
tial between  the  terminals  of  which  can  be  shown  even 
with  the  gold-leaf  electroscope. 

232.  The  Difference  of  Potential  between  the  Metals  of 
a  Voltaic  Cell  is  Independent  of  the  Size  of  the  Cell.  —  To 
verify  this  statement,  plunge  sheets  of  copper  and  zinc 
into  a  jar  containing  a  liter  or  more  of  dilute  sulphuric 
acid  (1  :  20,  or  thereabout).     Connect  these  with  wires  to 
the  quadrant  pairs  of  an  electrometer  of  the  simple  form 
described  in  Chapter  XXIV.     Note  the  deflection.     Then, 
with  shears,  cut  a  very  narrow  strip  from  each  of  the 
sheets  of  metal.     Dip  the  ends  of  these  into  a  drop  of 
acid,  remove  from  the  jar,  and  place  in  a  watchglass  or 
other  convenient  receptacle.     Connect  with  the  electrome- 
ter as  before,  and  note  that  the  deflection  is  as  large  as  in 
the  previous  case.     This  point  may  be  demonstrated,  also, 
and  more  conveniently,  by  means  of  the  galvanometer. 

233.  The  Electric  Current.  —  If  the  terminals  of  a  voltaic 
battery  be  connected  together  by  means  of  a  wire,  or  other 
conductor,  the  unlike  charges  which  have  been  gathered 
at  the  terminals  as  a  result  of  chemical  action  will  tend  to 
neutralize  each  other  precisely  as  opposite  charges  upon 
any  two  conductors  would  do  in  case  they  were  metalli- 
cally connected.     This  equalization  of  charge  may,  as  a 
matter  of  convenience,  be  considered  as  a  flow  of  electri- 
city through  the  connecting  wire,  and  we  may  say  that 


266  THE  OUTLINES  OF  PHYSICS 

the  direction  of  the  flow  is  from  the  positively  charged 
terminal  to  the  negatively  charged  terminal.  The  result 
is  what  we  call  the  electric  current.  One  very  important 
difference  between  the  cases  of  bodies  charged  by  friction 
and  bodies  charged  by  chemical  action  is  as  follows : 

When  two  bodies,  previously  given  opposite  charges  by 
friction,  are  brought  into  contact  with  one  another,  there  is 
immediately  an  instantaneous  exchange,  and  the  charges 
neutralize  each  other.  If  the  two  conductors,  however, 
form  terminals  of  a  voltaic  battery,  they  may  be  connected 
metallically,  and  the  difference  of  potential  between  them 
will  be  continually  maintained  by  chemical  action  going 
on  within  the  cells. 

The  flow  of  current  between  the  positive  and  negative 
terminal,  in  the  latter  case,  is  not  a  matter  of  short  dura- 
tion, as  in  the  case  of  two  conductors  which  have  been 
previously  charged,  and  which  discharge  themselves  upon 
contact,  but  will  continue  as  long  as  the  chemical  action 
continues.  The  existence  of  an  electric  current  shows 
itself  chiefly  in  the  following  ways : 

(1)  By  its  magnetic  action. 

(2)  By  its  thermal  action. 
(8)  By  its  chemical  action. 

234.    EXPERIMENT  70.  —  Phenomena  of  the  Simple  Cell. 

Apparatus  : 

(1)  A  glass  beaker  or  an  ordinary  tumbler. 

(2)  Strips  o&zinc  and  copper,  sulphuric  acid. 
Procedure  : 

(a)  Nearly  fill  the  glass  with  dilute  acid,  i.e.  ten  parts  of  water  to 
one  of  acid. 

(&)  Bend  the  strips  at  one  end  so  as  to  form  a  hook,  and  hang 
them  by  these  hooks  to  the  lip  of  the  glass.  Note  the  generation  of 
gas  at  the  surface  of  the  zinc.  If  collected  in  an  inverted  test  tube 
and  ignited,  this  gas  will  be  found  to  be  hydrogen. 


THE  ELECTE1C  CUEEENT 


267 


(c)   Lay  a  bit  of  naked  copper,  scraped  until  bright,  across  between 
the  strips  as  in  Fig.  228.1 

Note  that  a  change  in  the  generation  of  gas  immediately  follows,  and 
that  gas  bubbles  begin  to  appear  upon  the  copper  strip  as  well  as  upon 
the  zinc.    If  tested,  thes*e  gases  would 
likewise  be  found  to  consist  of  hy- 
drogen. 

As  soon  as  the  terminals  are  con- 
nected by  means  of  the  copper  wire, 
current  begins  to  flow.  The  direc- 
tion of  this  current  is  from  copper 
to  zinc  along  the  wire,  and  from 
zinc  to  copper  through  the  liquid. 

In  order  to  have  a  permanent  flow  there  must  be  a  completed,  or,  as 
we  say  in  electrical  terms,  a  closed  circuit.  This  current  is  maintained 
by  means  of  the  energy  generated  by  the  chemical  reaction  going  on 
within  the  cell.  It  has  just  been  noted  that  this  reaction  differs  when 
the  circuit  is  open  and  when  it  is  closed. 

Reaction  on  Open  Circuit.  —  The  zinc  is  attacked  by  the  sulphuric 
acid,  giving  as  a  product  zinc  sulphate,  i.e. 


FIG.  228. 


The  gas  is  given  off  at  the  surface  of  the  zinc. 

The  presence  of  the  copper  is  unnecessary  to  this  reaction. 

The  energy  of  the  reaction  is  converted  into  heat. 

If  the  zinc  be  amalgamated  by  rubbing  with  mercury,  the  reaction 
will  cease  altogether. 

Reaction  with  Closed  Circuit.  —  The  product  of  the  reaction  is  the 
same  as  before  ;  but  hydrogen  is  evolved  both  at  the  zinc  and  at  the 
copper  terminals. 

The  gas  evolved  at  the  zinc  pole  is  due  to  the  continuance  of  the 
open  circuit  reaction. 

If  the  zinc  be  amalgamated  the  evolution  at  the  copper  continues, 
while  that  at  the  zinc  ceases. 


1  This  figure  shows  the  apparatus  mounted  for  use  in  the  field  of  the 
lantern.  It  differs  from  the  arrangement  indicated  above  only  in  that 
the  liquid  is  contained  in  a  flat  cell  with  glass  sides  instead  of  a  cylindri- 
cal glass.  (See  Appendix  VII.) 


268  THE  OUTLINES   OF  PHYSICS 

The  energy  of  the  reaction  is  converted  into  electrical  energy  and 
is  a  source  of  electric  current. 

(c?)  Test  the  foregoing  statements  with  reference  to  the  effect  of 
amalgamation  of  the  zinc  upon  the  action  of  the  cell. 

235.  Polarization  of  the  Voltaic  Cell.  —  The  gathering  of 
gas  at  the  terminals  of  a  cell  is  detrimental  because  of  the 
greatly  increased  resistance  to  the  passage  of  the  current. 
The  hydrogen  upon  the  zinc  terminal  is  obviated  by  amal- 
gamation as  already  shown.     To  prevent  the  formation  of 
the  gas  upon  the  copper  terminal,  a  substance  containing 
loosely  combined  oxygen  is  added  to  the  liquid.     Such 
materials  are  called  depolarizers.      The    most  frequently 
employed  are  bichromate  of  potassium,  chromic  acid,  per- 
manganate of  potassium,  and  manganese  dioxide. 

A  cell  with  hydrogen  upon  the  copper  possesses  much 
less  difference  of  potential  between  its  terminals  than 
would  otherwise  be  the  case.  It  is  to  obviate  this  effect, 
which  is  called  polarization  and  which  is  more  important 
than  the  rise  in  the  resistance  of  the  cell,  that  the  de- 
polarizer is  employed. 

236.  Forms  of  the  Voltaic  Cell.  —  The  voltaic  cells  in 
common  use  are  of  two  types :  open  circuit  cells  and  closed 
circuit  cells. 

Properties  of  Open  Circuit  Cells.  —  These  cells  are  used 
for  the  production  of  momentary  currents  only,  with  con- 
siderable periods  of  rest  (for  operating  signals,  ringing 
bells,  etc.). 

They  suffer  polarization  when  continued  action  is  de- 
manded of  them. 

The  open  circuit  cell,  although  incapable  of 'furnishing 
strong  currents  continuously,  must  be  capable  of  respond- 


THE  ELECTRIC  CURRENT 


269 


ing  when  the  circuit  is  closed,  without  previous  prepara- 
tion, for  months  at  a  time. 

The  way  in  which  the  necessary  conditions  are  met  in 
the  Le  Clanche  cell,  which  is  a  typical  form,  is  as  follows : 

The  negative  terminal  is  a  rod  of  zinc.  This  is  immersed 
in  a  liquid  which  acts  upon  it  only  when  the  circuit  is  closed, 
i.e.  in  an  aqueous  solution  of  ammonium  chloride. 

The  positive  terminal  is  of  carbon.  It  is  surrounded 
with  dioxide  of  manganese,  which  acts  as  a  slow  depolar- 
izer. This  is  sometimes  packed  into  a  porous  cup  together 
with  the  carbon ;  sometimes  it  is  compressed  into  blocks, 
as  in  the  figure,  which  are  attached  to  the  carbon  by  means 
of  rubber  bands. 

The  jar  is  closed  to  hinder  evaporation. 

Figure  229  is  a  sketch  of  the  Le  Clanche  cell. 

Properties  of  Closed  Circuit  Cells.  —  These  cells  must 
be  capable  of  furnishing  strong  currents  continuously  for 


FIG.  229. 


FIG.  230. 


considerable  intervals  of  time.     The  conditions  to  be  met, 
therefore,  are  low  resistance  and  prompt  depolarization. 

In  the  bichromate  cell  (Fig.  230),  which  is  one  of  the 
best-known  forms  of  closed  circuit  cells,  the  positive  ter- 


270 


THE  OUTLINES   OF  PHYSICS 


minal  consists  of  two  parallel  slabs  of  carbon  which  are 
metallically  connected  at  the  top.  Between  these  is  the 
negative  terminal,  a  plate  of  zinc.  The  large  surfaces  of 
these,  and  their  proximity,  secure  very  low  resistance. 

The  liquid  is  dilute  sulphuric  acid  in  which  potassium 
bichromate  has  been  dissolved.  The  chromic  acid  thus 

formed  in  the  solution 
gives  up  a  portion  of  its 
oxygen  to  the  hydrogen, 
as  fast  as  the  latter  ap- 
pears. It  thus  acts  as  a 
very  prompt  depolarizer. 

This  liquid  acts  upon 
zinc,  even  when  the  cir- 
cuit is  open.  It  is  neces- 
sary, therefore,  to  with- 
draw the  zinc  when  the 
battery  is  not  in  use;  this 
is  accomplished  bv  means 

FIG.  231.  ,          ,.  ,. 

of  a  sliding  rod,  as  shown 

in  the  figure.  Sometimes  a  battery  consisting  of  several 
bichromate  cells  are  arranged  so  that  all  the  zincs  may 
be  raised  or  lowered  simultaneously.  (See  Fig.  231.) 
Such  an  arrangement  is  called  a  plunge  lattery.1 

1  For  a  full  discussion  of  the  voltaic  cell  and  for  a  description  of  numer- 
ous forms  to  which  no  reference  is  made  here,  see  Carhart,  Primary  Bat- 
teries ;  see  also  Elements  of  Physics,  Vol.  II,  Chap.  V. 


• 

MAGNETIC  EFFECTS   OF  THE  CURRENT  271 


CHAPTER   XXVII 

THE   MAGNETIC  EFFECTS   OF   THE   CURRENT 

237.  Preliminary  Observations  concerning  the  Magnetic 
Effect  of  the  Current.  —  If  several  cells  of  the  bichromate 
battery  described  in  Art.  237  be  placed  in  series,  and  the 
terminals  of  the  battery  thus  formed  be  connected  by 
means  of  a  copper  wire,  a  strong  current  of  electricity 
will  flow  through  this  wire  from  the  positive  to  the  nega- 
tive terminal  of  the  battery.  If  this  wire  passes  through 
a  hole  in  the  center  of  a  flat  block  of  wood, 
as  shown  in  Fig.  232,  and  if  the  upper  sur- 
face of  the  block  which  should  previously 
have  been  covered  with  glazed  paper  or  card- 
board be  strewn  with  fine  iron  filings,  these 
will  be  seen  to  arrange  themselves  in  con- 
centric circles,  with  the  axis  of  the  wire  as  a 

center.      Figure    233, 

which  is  from  a  photo- 

graph,   shows   the   ar- 

rangement  of  iron  fil- 


i  FIG.  232. 

ings    in   such   a   case. 
Each  particle    of  iron  in  the  neigh- 
borhood  of   the   electric  current  be- 
comes  a'  magnet.     The  entire  region 
around  a  wire  which  carries  an  elec- 
tric   current    becomes    what   is    called   a   magnetic  field. 
In  this  field  forces  are  at  work  which  tend  to  move  the 
poles  of   any  magnet  which  may  be   in    the   field   along 


272  THE  OUTLINES   OF  PHYSICS 

certain  lines  which  are  called  lines  of  force.  The  minute 
magnets  formed  from  the  iron  filings  are  acted  upon  by 
.these  forces  in  such  a  way  as  to  cause  them  to  arrange 
themselves  in  the  lines  of  force.  The  lines  of  force 
around  a  straight  wire  through  which  current  passes  are 
circles. 


238.    EXPERIMENT  71.—  Magnetic  Field  of  a  Coil  of  Wire  through 
which  Current  flows. 

Apparatus  : 

(1)  Six  cells  of  bichromate  battery  arranged  as  described  in  the 
previous  article. 

(2)  A  hollow  cylinder  about  15  cm.  long  and  3  cm.  in  diameter. 

A  cylindrical  glass  lamp  chimney  such  as  is  used  with  the  Argand 
burner  may  be  employed. 

(3)  Several  meters  of  copper  wire.     The  insulated  wire  known  as 
annunciator  wire  or  office  wire,  size  No.  18  or  20,  is  well  adapted  for 
this  experiment. 

Procedure : 

(a)  Wrap  the  cylinder  carefully  from  end  to  end  with  wire.     One 
layer  will  suffice.     Secure  the  layer  in  its  place  by  means  of  threads 
passed  through  the  cylinder  and  tied.     The  coil  thus  formed  is  called 
a  helix  or  solenoid. 

(b)  Cut  two  pieces  of  stiff  cardboard  20  cm.  square  into  the  form 
shown  in  Fig.  234,  and  trim  the  tongue  of  each  piece  so  that  it  will 
fit  the  inside  of  the  cylinder.     Touch  the  tongue  of  each  with  muci- 
lage, and  insert  in  the 
cylinder  in  such  a  way 
that  the  flat  portions 
will    afford    platforms 
opposite  the  mouths  of 

the  cylinder  as  shown 
FIG.  234.  FIG.  235.  .Q  Fig   235 

(c)  After  the  apparatus  is  dried,  mount  the  coil  with  its  axis  hori- 
zontal, and  the  two  platforms  of  cardboard  also  in  a  horizontal  plane. 
Send  the  current  through  the  coil,  and  strew  filings  upon  the  card- 
board.    Note  the  tendency  of  the  filings  to  arrange  themselves  along 


MAGNETIC  EFFECTS   OF  THE  CURRENT  273 

lines  of  force.  This  tendency  may  be  increased  by  tapping  the  card- 
board. The  arrangement  will  be  that  shown  in  Fig.  236.  Note  that 
all  the  lines  of  force  appear  to  enter  the  mouth  of  the  cylinder :  in 
point  of  fact,  if  we  were  to  trace  the 
lines  of  force  throughout,  we  should 
find  that  they  entered  the  cylinder  at 
one  end,  passed  through  its  entire 
length,  and  issued  from  the  other ;  also 
that  they  returned  through  the  outer 
atmosphere,  forming  a  closed  curve. 
It  may  be  laid  down  as  a  general  law 
that  all  magnetic  lines  of  force  are  pIG  235. 

closed  curves.    The  arrangement  of  the 

filings  observed  in  this  experiment  indicates  the  character  of  a  plane 
section  of  the  field  produced  by  the  coil  of  wire.  In  the  neighbor- 
hood of  such  a  coil  through  which  current  flows,  all  iron  tends  to 
become  magnetized.  This  fact  shows  itself  most  strongly  in  the  case 
of  pieces  of  that  metal  which  are  inserted  within  the  cylinder  itself, 
because  in  that  region  the  number  of  lines  of  force  are  greatest. 

239.  EXPERIMENT  72.  —  Magnetization  of  Iron  by  Means  of  a 
Solenoid. 

Apparatus : 

(1)  The  battery  or  solenoid  described  in  the  previous  article. 

(2)  A  bar  of  soft  Norway  iron  about  1  cm.  in  diameter  and  5  cm. 
longer  than  the  solenoid.  ,;, 

Procedure : 

(a)  By  means  of  two  pieces  of  gummed  paper  fasten  the  soft  iron 
bar  as  nearly  as  possible  in  the  axis  of  the  solenoid,  immediately 
below  the  cardboard  platforms.  Let  its  ends  project  equally  from 
the  coil. 

(&)  Send  the  current  through  the  coil  and  map  the  field  of  force 
by  means  of  iron  filings  as  in  the  previous  experiment. 

(c)  Note  that  the  lines  of  force  now  nearly  all  appear  to  enter  the 
iron.  Compare  the  character  of  the  field  —  which  will  be  similar  to' 
that  shown  in  Fig.  237  with  that  obtained  in  the  previous  experi- 
ment. The  iron  bar  has  become  for  the  time  being  a  magnet,  and 
the  regions  in  the  ends  where  the  lines  of  force  enter  the  iron  from 
the  outer  air  are  called  magnetic  poles. 
T 


274  THE  OUTLINES   OF  PHYSICS 

If  we  consider  the  lines  of  force  to  be  closed  curves,  entering  the 
iron  and  the  core  at  one  end  and  issuing  from  the  other,  we  have  the 
means  of  distinguishing  between  the  two  poles  of  the  magnet.  One 

of  these  is  called  the  north  pole  of  the 


There  is  a  general  agreement  among 
physicists  to  consider  the  lines  of  force 
as  issuing  from  the  north  pole  and  en- 

'i'^:^^^:''-:'-^'^':^''''^^^^     tering  at  the  south  pole..    The  names 
^^iH-^cJi-        """••-.•'-".—  V."  -^5     of  these  poles   are   derived  from   the 
'"••"•'  :  ''r^.      behavior  of  magnets  when  suspended 
FIG  237  *n  ^ne  mag'netic  field  of  the  earth. 

(W)  Turn  the  solenoid  over  so  that 

the  bar  of  iron  is  above  the  cardboard.  Send  the  current  through  it 
again,  and  strew  filings.  Note  how  the  filings  cling  to  the  iron, 
especially  in  the  regions  which  have  already  been  described  as  poles  ; 
note  further  that  the  filings  tend  to  attach  themselves  to  the  mag- 
netized poles  endwise,  proceeding  from  the  poles  outward.  Note  that 
each  one  tends  to  set  itself  in  the  direction  of  a  line  of  force. 

(e)  Remove  the  bar  from  the  solenoid,  and  notice  that  the  ten- 
dency of  the  iron  filings  to  cling  to  its  poles  decreases,  and  when  the 
bar  has  been  entirely  withdrawn  ceases  altogether.  (If  the  iron  used 
in  this  experiment  is  not  soft,  this  last  statement  will  not  be  found  to 
be  quite  true.  The  pole  will  remain  slightly  magnetized,  for  reasons 
which  are  described  in  the  following  articles.)  The  magnetization  of 
the  soft  iron  bar,  which  it  has  been  the  object  of  this  experiment 
to  consider,  is  called  temporary  magnetization  :  it  depends  for  its  exist- 
ence upon  bringing  the  iron  into  the  magnetic  field,  and  it  lasts  only 
so  long  as  the  iron  remains  in  that  field. 

The  term  permanent  magnetization,  on  the  other  hand,  is  used  to 
designate  the  lasting  effect  produced  upon  the  properties  of  steel,  and 
of  various  hardened  varieties  of  iron,  by  the  action  of  the  magnetic 
field.  The  intensity  of  permanent  magnetization  is  usually  small  as 
compared  with  that  of  the  temporary  magnetization  produced  by  the 
Same  field.  It  varies  greatly  with  the  temper  of  the  metal.  Per- 
manent magnetization  varies  with  the  temperature  of  the  magnet.  It 
diminishes  as  the  temperature  rises  ;  and  finally,  when  a  certain  point 
called  the  critical  temperature  is  reached,  the  iron  (or  steel)  becomes 
non-magnetic.  The  critical  temperature  for  steel  is  about  735°  C. 


MAGNETIC  EFFECTS   OF  THE  CURRENT  275 

240.    EXPERIMENT    73.  —  Permanent  Magnetization  of  Steel  by 
means  of  a  Solenoid. 

Apparatus : 

(1)  The  battery  and  solenoid  described  in  the  previous  experi- 
ments. 

(2)  Six  steel  knitting  needles,  which  should  be  somewhat  longer 
than  the  solenoid,  also  several  sewing  needles. 

Procedure : 

(a)  Connect  the  solenoid  with  the  terminals  of  the  battery,  noting 
the  direction  in  which  the  current 
flows  through  the  wire;  that  is  to 
say,  start  at  the  copper  or  carbon 
pole  of  the  battery,  which  is  called 
the  positive  pole,  and  consider  that 
the  current  flows  from  that  through 
the  coil  to  the  zinc  pole.  (See  Fig.  FIG.  238. 

238.) 

(ft)  Insert  one  of  the  sewing  needles  into  a  small  cork,  pushing  it 
through  until  the  cork  reaches  the  middle  of  the  needle. 

(c)  Face   the   solenoid,  looking  toward  that  end  of  it  at  which 
the    current    is    traversing    the    turns    clockwise    (Fig.    239),    and 
insert  the  needle,  point  first,  into  the  axis  of  the 

coil.     In  this  pesition  the  needle  will  afford  a  path 

for  the  passage  of  lines  of  force  through  the  coil. 

The  region   where  the   lines  of  force  enter  will 

become  a  south-seeking  pole;  the  region  where  the 

lines  issue  from  the  steel  into  the  air  again  will 

become  a  north-seeking  pole.     In  short,  the  needle  will  become  a 

magnet.     These  two  regions  lie,  of  course,  very  near  the  ends  of  the 

needle.     Steel  differs  from  soft  iron  in  that  it  is  capable  of  retaining 

its  magnetized  condition  after  being  withdrawn  from  the  field  of  the 

coil. 

(d)  To  test  this  statement,  tap  the  needle  sharply  three  or  four 
times  with  the  end  of  a  pencil  or  other  piece  of  wood,  and  remove  it 
from  the  coil.     Withdraw  the  cork,  and  place  the  needle  beneath  a 
piece  of  stiff  paper  or  cardboard,  strew  iron  filings  upon  the  surface 
of  the  paper,  and  note  the  arrangement  of  them.     It  will  be  seen  that 
they  tend  to  arrange  themselves  as  shown  in  Fig.  240. 

The  pattern  indicates  the  trend  of  the  lines  of  force.     It  is  that 


276  THE  OUTLINES   OF  PHYSICS 

which  one  would  expect  from  a  magnet  with  poles  near  the  ends 
of  the  needle. 

(e)  Drop  the  magnetized  needle  lightly  upon  the  surface  of  a  dish 
of  water.     If  this  operation  is  performed  in  such  a  way  that  the 

needle  strikes   the  water 


\-    ;  -''       with  its  axis  parallel  to 


\\  '    -,  •',-  >  .  t^ .  '  ''7~   ;\  .^  *'  1 1'.'.}  '///-'A      the  surface,  it  will  be  sus- 
^•V'Y'  ^-'*y  ••     tained     by    the     surface 
.,'.'>.''•'  /'•*?•     film',  and  will  float.    Note 
*. ,'l> '"-;:/ '^-t-'      that  it  immediately  sets 
^  r^'i-  .^      itself  nearly  into  a  north 
f-?;v'x;>S»      and  south  position,  with 
.  I  i'<vXVC  \      the  point  northward. 
',•1  \,  >/••; ')  .*;    > V. ^~1'^>"-  /•//  • ',» '  J.V  V^Cr  Cy)  Insei"t     into     the 

f'f\j)f.y\.'i^;^^:**",/~'si',f''>'t?\<\t.\*       coil,    through  which  the 
"  Fir  ^0  current  is  flowing  as  be- 

fore, one  of  the  knitting- 
needles.  Tap  the  latter  sharply  with  a  block  of  wood,  and  withdraw 
it  from  the  coil :  it  also  has  become  a  permanent  magnet.  Bring 
it  into  the  neighborhood  of  the  floating  sewing  needle.  Note  that 
the  end  of  the  magnetized  knitting  needle  which  corresponded  in 
position,  when  within  the  coil,  with  the  point  of  the  sewing  needle, 
and  which  has  likewise  been  made  a  north-seeking  pole,  attracts 
the  eye  end  of  the  magnetized  needle  and 
repels  its  point  (Fig.  241).  Note  that  the 
other  end  of  the  knitting  needle,  which  has 
been  made  into  a  south-seeking  pole,  attracts 
the  point  and  repels  the  eye  end  of  the  float- 
ing needle.  From  this  observation  we  con- 
clude that  like  magnetic  poles  repel  each 
other,  and  unlike  attract  each  other. 

To  test  this  matter  further,  remove  the 
magnetized  needle  from  the  dish  of  water, 
FIG.  241  an(^  replace  it  with  a  needle  which  has  not 

been    magnetized.      Note    that    the    latter 

possesses  but  little  if  any  tendency  to  set  itself  in  a  north  and  south 
direction ;  furthermore,  that  either  end  of  it  will  be  attracted  by  the 
magnetized  knitting  needle,  or  by  either  end  of  the  magnetized 
sewing  needle.  (To  succeed  in  this  portion  of  the  experiment,  it  is 


MAGNETIC  EFFECTS  OF  THE  CURRENT  277 

necessary  to  take  some  precautions  to  prevent  the  sewing  needles 
from  becoming  slightly  magnetized;  in  other  words,  they  must  be 
kept  away  from  all  magnetizing  bodies  and  from  the  magnetizing 
coil.) 

(</)  Magnetize  two  more  sewing  needles  in  the  manner  described 
in  (6)  and  (c)  of  this  experiment.  Float  these  three  needles  on 
different  parts  of  the  dish  of  water  and  watch  their  behavior.  It  will 
be  seen  that  they  drift  slowly  together,  turning  so  as  to  arrange  them- 
selves side  by  side  with  unlike  poles  in  contact. 

241.  Action  of  a  Wire,  bearing  Current,  upon  a  Magnet. 
—  It  has  already  been  shown  that  any  wire  which  carries 

an  electric  current  possesses  a  magnetic  field.  If  we 
bring  such  a  wire  near  to  a  magnet,  forces  are  brought 
into  action  between  the  two.  These  may  be  considered  to 
be  due  to  the  mutual  action  between  the  lines  of  force  of 
the  two  fields.  It  is  as  though  lines  of  force  running  in 
the  same  direction  tended  to  repel  each  other.  If  the 
magnet  have  freedom  of  motion,  it  will  tend  to  set  itself 
in  such  a  position  that  its  lines  of  force  are  parallel  to 
those  which  surround  the  current.  This  action,  which 
may  readily  be  shown  by  means  of  the  floating  needle, 
forms  the  basis  for  the  instrument  known  as  the  galva- 
nometer. It  is  well  illustrated  by  means  of  the  following 
experiment : 

242.  EXPERIMENT  74.  —  Magnetic  Influence  of  a  Wire,  carrying 
Current,  upon  a  Floating  Needle. 

Apparatus  : 

(1)  The  floating  needle  previously  described,  a  cell  of  battery, 
three  or  four  meters  of  copper  wire. 

Procedure : 

(a)  Connect  the  wire  to  the  terminals  of  the  battery,  and  hold 
about  a  half  meter  of  the  intervening  portion  of  the  same  in  the 
hands.  Bring  this  part  of  the  wire  near  to  the  needle,  holding  it 
above  the  latter  in  a  horizontal  position,  and  as  nearly  as  possible  in 


278 


THE  OUTLINES  OF  PHYSICS 


FIG.  242. 


a  north  and  south  plane.     Note  that  the  needle  is  deflected  from  its 
north  and  south  position  in  the  earth's  field. 

The  direction  towards  which  the  north-seeking  pole  tends  is  east- 
erly or  westerly,  according  to  the 
direction  in  which  the  current  flows 
through  the  wire.  If  the  current 
flows  toward  the  north,  that  is  to 
say,  if  the  end  of  the  wire  which  is 
towards  the  south  is  attached  to  the 
copper  terminal  of  the  battery,  and 
the  northerly  end  to  the  zinc  ter- 
minal (see  Fig.  242),  the  north- 
seeking  end  of  the  floating  needle 
will  tend  to  point  towards  the  west. 
If  the  current  is  reversed,  the  north-seeking  pole  will  point  toward 
the  east.  But  for  the  forces  due  to  the  earth's  field,  the  magnetic 
needle  would  always  point  directly  at  right 
angles  to  the  wire  which  carries  the  current. 
On  account  of  the  earth's  magnetism  it 
comes  to  rest,  however,  in  the  position 
where  the  forces  of  the  earth's  field  are 
precisely  balanced  by  those  due  to  the  action 
of  the  current.  (See  Fig.  243.)  To  test 
this  statement,  proceed  as  follows : 

(&)  Turn  the  ends  which  hold  the  wire 
m-ent  in  such  a  way  as  to  swing  the  wire  round 
into  an  east  and  west  direction,  and  note 
that  in  this  way  the  action  upon  the  needle 
diminishes,  becomes  zero,  and  as  the  wire  is 
brought  around  into  a  north  and  south 
direction  with  its  end  reversed,  begins  to  show  a  deflection  with  its 
north  pole  towards  the  east.  Move  the  wire  from  the  neighborhood 
of  the  needle,  and  bring  it  up  again  from  below :  note  that  now  all 
the  above  effects  are  reversed. 

(c)  Coil  the  wire  into  a  large  circular  loop.  Hold  this  loop  in  a 
north  and  south  vertical  plane  and  move  it  up  slowly  towards  the 
needle  from  the  east.  Note  the  deflection  which  occurs,  and  that  it 
increases  until  the  wire  is  in  the  same  plane  with  the  needle,  and  then 
begins  to  diminish  again  as  the  wire  moves  westward. 


force 
due  to 
cur 


force  due  to  earth's  field 
FIG.  243. 


MAGNETIC  EFFECTS   OF  THE  CURRENT  279 

243.   Ampere's  Rule.  —  The  action  of  a  wire  carrying 
current  upon  a  magnetic  needle  was  first  de- 
scribed by  Oersted  in  1819.     The  effect  was 
later  stated  by  the  French  physicist  Ampere, 
as  follows : 

If  one  imagine  himself  swimming  with  the 
current  and  facing  the  needle,  the  north-seeking 
pole  will  always  be  deflected  towards  his  left 
hand. 

Many  persons  prefer  the  following  simple 
rule : 

Hold  the  right  hand  with  the  thumb  extended 
(Fig.  244),  the  fingers  pointing  in  the  direction 
in  which  the  current  flows  and  the  palm  towards 
the  needle.  The  north-seeking  pole  will  be  de- 
flected towards  the  thumb.  FIG.  244. 


280  THE  OUTLINES  OF  PHYSICS 


CHAPTER   XXVIII 

MAGNETISM 

244.  The  Earth's  Magnetic  Field. —  The  experiments  with 
the  floating  magnet  described  in  the  preceding  chapter, 
illustrate  several  important  points  in  the  science  of  mag- 
netism. The  floating  needle  acts  as  a  magnetic  compass, 
pointing  with  its  north-seeking  pole  towards  the  magnetic 
north  pole  of  the  earth.  The  behavior  of  magnet  needles 
at  various  points  upon  the  surface  of  the  planet  indicate 
that  the  earth  itself  may  be  considered  as  a  magnet  and 
that  the  surface  of  the  earth  lies  within  a  magnetic  field 
consisting  of  lines  of  force  which  issue  from  one  of  the 
earth's  poles  and  return  through  space  to  the  other.  In 
the  neighborhood  of  the  equator  these  lines  are  nearly  hori- 
zontal. As  we  approach  the  poles  of  the  earth,  they  dip 
downward  more  and  more,  until  finally,  if  one  could  take 
up  his  position  at  a  point  immediately  over  the  magnetic 
north  pole,  or  the  magnetic  south  pole,  he  would  find  the 
lines  of  force  vertical.  In  latitude  40°  N.  in  the  Western 
Hemisphere  this  dip  of  the  lines  of  force  is  about  70°. 

The  directive  force  which  causes  the  compass  needle  to 
point  towards  the  earth's  north  pole  is  the  horizontal  com- 
ponent of  these  lines  of  force.  If  the  needle  were  free 
to  revolve  upon  a  horizontal  axis  also,  it  would  come  to 
rest  in  a  position  making  an  angle  of  about  70°,  as  has 
already  been  indicated,  with  the  horizon.  The  north- 
seeking  pole  would  point  downward  and  northward  at  the 
same  time. 


MAGNETISM  281 

245.  The  Dipping  Needle.  —  An  instrument  by  means  of 
which  the  amount  of  dip  may  be  determined  is  called  a 
dipping  needle.     It  consists  of  a  bar  of  steel  (Fig.  245), 
through  which  is  placed  a  transverse   axle 

which  passes  accurately  through  the  center 
of  gravity  of  the  bar.  If  the  bar  is  not  mag- 
netized, it  will  be  in  indifferent  equilibrium 
when  mounted  upon  this  axle.  If  it  be 
magnetized,  and  then  mounted  upon  the  hori- 
zontal axle,  the  end  that  contains  the  north- 
seeking  pole  will  immediately  dip  downward, 
as  though  mass  had  been  added  to  it.  The 
reason  for  this  change  in  its  behavior  is  that 
the  needle  is  now  in  a  condition  to  have  its 
poles  attracted  and  repelled  by  the  magnetic 
force  of  the  earth,  and  it  tends  to  come  to 
rest  in  the  lines  of  force  of  the  earth's  field.  Since  the 
bar  has  freedom  of  rotation  around  a  horizontal  axis,  it  is 
in  equilibrium  only  when  it  dips  into  a  position  such  that 
the  lines  of  force  are  parallel  to  the  line  joining  its  north 
and  south  seeking  poles.  If  we  measure  the  angle  which 
such  a  needle  makes  with  the  horizon,  we  shall  have  de- 
termined the  angle  of  dip  for  the  locality  in  which  the 
needle  is  mounted. 

246.  The  Nature  of  a  Magnetic  Pole.  —  It  is  often  assumed 
for  convenience  that  a  magnetic  pole  is  a  point  lying  within 
a  magnet,  generally  near  one  end.    A  better  definition  con- 
siders the  pole  to  be  that  region  of  a  magnet  where  lines  of 
force  leave  the  iron  and  enter  the  air,  or  vice  versa. 

Iron  affords  a  better  path  for  the  lines  of  force  than  the 
air  does,  so  that  they  tend  to  continue  within  the  iron  of 
a  bar  magnet  until  the  end  is  reached.  Then  they  are 


282  THE  OUTLINES  OF  PHYSICS 

forced  outward  into  the  air.  If  a  piece  of  iron  be  strongly 
magnetized,  this  region  throughout  which  lines  of  force 
are  leaving  the  iron  is  quite  an  extended  one,  so  that  the 
pole  must  be  considered  as  distributed  throughout  the 
entire  end  of  the  bar,  instead  of  being  concentrated  at  a 
single  point.  Figure  246  shows  the  arrangement  of  the  lines 


FIG.  246. 

of  force  around  a  bar  magnet  as  indicated  by  the  pattern 
in  which  iron  filings  group  themselves.  It  will  be  seen 
that  everywhere  near  the  ends  of  the  bar  lines  of  force  are 
leaving  the  iron  and  entering  the  air,  and  that  it  would 
be  a  matter  of  great  difficulty  to  fix  upon  any  given  point 
which  could  be  regarded  as  the  location  of  the  pole.  The 
significance  of  this  definition  of  a  magnetic  pole  may  be 
illustrated  by  means  of  the  following  experiment  : 

247.   EXPERIMENT  75.  — Making  Magnets  by  the  Breaking  of  a 
Magnetized  Bar. 

Apparatus  : 

(1)  A  steel  knitting  needle,  a  pane  of  window  glass,  and  some  iron 
filings. 

(2)  A  battery  and  a  coil  of  wire. 

(3)  A  dish  of  water  and  a  magnetized  sewing  needle  (described  in 
Art.  240). 


MAGNETISM  283 

Procedure : 

(a)  Connect  the  coil  of  wire  in  circuit  with  three  or  four  cells  of 
the  battery.  Insert  the  knitting  needle  in  the  coil,  so  that  it  lies  with 
the  coil  midway  between  its  ends.  Tap  the  needle  sharply  several 
times  with  a  block  of  wood  to  assist  in  the  rearrangement  of  the  mole- 
cules, and  then  break  circuit  through  the  coil. 

(&)  Float  the  magnetized  sewing  needle  upon  the  dish  of  water  as 
described  in  Experiment  72.  Bring  the  knitting  needle  near,  and 
determine  the  character  of  its  poles  by  the  attraction  or  repulsion  of 
the  north-seeking  pole  of  the  floating  needle.  Mark  the  north-seeking 
pole  of  the  knitting  needle  in  any  convenient  way,  either  by  attaching 
a  bit  of  gummed  paper  to  it,  or  by  touching  it  with  ink. 

(c)  Break  the  knitting  needle  in  half,  and  test  the  magnetization 
of  each  piece  by  means  of  the  floating  needle.  Note  that  the  broken 
ends  have  each  acquired  a  magnetic  pole,  that  these  poles  are  dissimi- 
lar, and  that  the  new  pole  which  is  in  the  piece  which  contains  the 
original  north-seeking  pole  of  the  needle  is  a  south-seeking  pole. 
Each  piece  of  the  knitting  needle  has,  in  a  word,  become  a  complete 
magnet  by  itself. 

The  formation  of  the  new  poles  may  be  explained  simply  from  the 
consideration  that  the  lines  of  force  which  previously  traversed  the 
needle  from  end  to  end  through  the  iron  were  forced  to  leave  the  iron 
at  the  point  of  rupture  as  soon  as  the  needle  was  broken. 

(rf)  Lay  the  two  pieces  of  the  broken  knitting  needle  in  the  same 
straight  line,  with  an  air  gap  of  2  cm.  between  the  broken  ends. 
Place  over  them  the  pane  of  glass,  wedging  the  latter  up  into  a 
horizontal  position  by  means  of  bits  of  wood.  Strew  the  glass  lightly 


FIG.  247. 


284 


THE  OUTLINES   OF  PHYSICS 


with  iron  filings  and  tap  it  several  times.     The   filings  will   adjust 
themselves  into  a  pattern  (Fig.  247),  which   indicates  quite  clearly 

the  character  of  the  magnetic  field. 
It  will  be  seen  from  the  accompany- 
ing diagram,  247  a,  that  there  are 
lines  of  force  emanating  from  and 
entering  the  iron  in  the  regions 
where  the  original  poles  were,  and 
likewise  at  the  new  ends  formed  by  breaking  the  needles. 

(e)  Break  each  half  of  the  knitting  needle  again  into  two  pieces, 
and  repeat  the  operation  described  in  (c)  and  (d).  It  will  be  found 
that  each  of  the  new  pieces  is  a  separate  magnet  by  itself.  The 
character  of  the  field  obtained  by  mapping  with  filings  the  four  pieces 


FIG.  247  a. 


FIG.  248. 


laid  end  to  end  with  intervening  air  gaps,  is  indicated  in  Fig.  248  and 
in  the  accompanying  diagram,  248  a.  Each  piece  of  the  original 
needle  will  have  a  north  and  a  south  seeking  pole.  These  will  all 


be  of  equal  strength,  so  that,  if  the  needle  could  be  restored,  the  poles 
at  each  point  of  rupture  being  equal  and  opposite  in  character,  would 
precisely  neutralize  one  another,  pairwise  throughout. 

248.  Magnetization  by  Induction.  —  Any  piece  of  iron 
placed  in  a  magnetic  field  becomes  a  magnet,  because  lines 
of  force  enter  it  to  find  a  better  path  than  is  afforded  by 
the  air,  and  leave  it  again  at  some  other  point.  The  region 


MAGNETISM 


285 


where  the  lines  of  force  of  the  field  in  which  the  piece  of 
iron  is  placed  enter  it  becomes  a  north-seeking  pole,  and 
the  region  where  they  forsake  the  iron  again  becomes  a 
south-seeking  pole.  Even  a  weak  field  like  that  of  the 
earth  is  capable  of  producing  such  an  effect.  This  may 
be  readily  shown  by  means  of  the  following  experiment : 

249.    EXPERIMENT  76.  —  Magnetization  of  a  Bar  of  Iron  by  means 
of  the  Earth's  Field. 

Apparatus  : 

(1)  A  bar  of  soft  iron  20  cm.  or  more  in  length. 

(2)  A  dish  of  water,  and  the  floating  needle  previously  described. 

Procedure: 

(a)  Float  the  magnetized  needle  upon  a  dish  of  water,  and  allow  it 
to  come  to  rest  in  its  north  and  south  direction.  Hold  the  bar  of  iron 
as  nearly  as  possible  in  the  lines  of  force  of  the  earth's  field ;  namely, 
with  one  end  pointing  northward  and  downward  at  an  angle  of  about 
70°.  Keeping  the  bar  in  its  position,  move  it  gradually  towards  the 
floating  needle.  It  will  be  found  that  the  lower  end  of  the  bar  has 
become  a  north-seeking  pole, 
and  that  the  north-seeking  pole 
of  the  floating  needle  is  re- 
pelled by  it  (Fig.  249).  Keep- 
ing this  end  of  the  bar  as 
nearly  as  possible  in  its  posi- 
tion, swing  the  other  end 
round  so  as  to  bring  the  bar 
into  an  east  and  west  position, 
where  it  will  be  at  right  angles 
to  the  lines  of  the  earth's  field. 
Note  that  its  repellent  power 
upon  the  north-seeking  pole  of 
the  floating  needle  is  thereby 
gradually  destroyed.  Continue 
these  movements  until  the  pole 


FIG.  249. 


FIG.  250. 


is  again  parallel  to  the  earth's 

field,  but  with  its  other  end  downward ;  namely,  in  the  position  shown 

in  Fig.  250. 


286  THE  OUTLINES   OF  PHYSICS 

The  end  which,  when  it  was  down,  became  a  north-seeking  pole 
has  now  become  a  south-seeking  pole,  by  virtue  of  its  change  of 
position,  and  it  attracts  instead  of  repelling  the  north-seeking  pole  of 
the  floating  needle.  Whereas  the  lines  of  force  which  issue  from  the 
north  pole  of  the  earth  entered  this  end  of  the  bar  in  its  former  posi- 
tion, thus  constituting  it  a  north-seeking  pole,  they  now  issue  from  it, 
so  that  its  character  is  the  same  as  the  north  pole  of  the  earth.  The 
pole  which  has  the  same  character  as  the  north  pole  of  the  earth  is 
therefore  repelled  by  it,  or,  in  other  words,  it  is  a  south-seeking  pole. 

(J)  In  the  case  of  soft  iron  this  action  of  the  earth's  field  is  almost 
entirely  temporary.  If  the  iron  be  not  perfectly  soft,  however,  perma- 
nent magnetization  may  be  brought  about  by  the  action  of  the  earth's 
lines.  To  test  this  point  hold  the  bar  of  iron  parallel  to  the  lines  of 
the  earth's  field,  and  tap  the  end  of  it  sharply  with  a  bit  of  wood  several 
times.  This  operation  may  be  performed  at  a  distance  from  the  float- 
ing needle.  Now  bring  the  bar  into  the  neighborhood  of  the  floating 
needle  and  test  it  for  magnetization.  It  will  probably  be  found  that 
it  has  acquired  a  permanent  north-seeking  pole  at  the  end  where  the 
blows  were  delivered,  and  a  south-seeking  pole  at  the  other  end.  The 
difference  between  these  permanent  poles  and  the  temporary  ones  pro- 
duced in  the  previous  portion  of  this  experiment  consists  in  the  fact 
that  the  former  are  independent  of  the  position  of  the  bar  in  the 
earth's  field,  whereas  the  latter  depended  upon  its  position. 

(c)  These  permanent  poles  may  be  destroyed  by  reversion  of  the 
process  which  produced  them,  and  the  magnetization  of  the  pole  may 
be  reversed  by  a  repetition  of  this  process. 

To  test  this  statement,  hold  the  magnetized  bar  near  the  floating 
needle  with  its  south-pointing  pole  downwards  and  with  the  axis  of 
the  pole  parallel  to  the  lines  of  force  of  the  earth's  field.  The  floating 
needle  will  have  its  north-seeking  pole  attracted.  Tap  the  upper  end 
of  the  bar  briskly  while  holding  it  in  this  position.  Note  that  with 
each  blow  the  attraction  upon  the  south-seeking  pole  of  the  floating 
needle  is  diminished  and  that  presently,  instead  of  being  attracted, 
the  latter  is  repelled.  The  meaning  of  this  is  that  the  south-seeking 
pole  has  been  neutralized  and  then  converted  into  a  north-seeking 
pole. 

250.  Permeability.  —  Mention  has  already  been  made 
of  the  fact  that  iron  affords  a  better  path  for  lines  of 


MAGNETISM  287 

force  than  is  offered  by  the  air.  The  name  given  to  this 
property  is  permeability.  It  is  measured  by  comparing 
the  number  of  lines  which  pass  through  iron  under  a 
given  magnetizing  force,  per  square  centimeter  of  cross- 
section,  with  those  produced  in  air  by  the  same  force. 

The  fact  of  the  high  permeability  of  iron  may  be  demon- 
strated as  follows : 

251.  EXPERIMENT  77.  —  Influence  of  an  Iron  Core  upon  the 
Strength  of  Field  of  a  Coil. 

Apparatus : 

(1)  A  dish  of  water  and  floating  magnet  needle. 

(2)  A  coil  of  wire  similar  to  that  used  in  Experiment  70  (Art.  238). 

(3)  A  rod  of  iron,  or  a  bundle  of  iron  wires  about  as  long  as  the 
Argand  chimney  upon  which  the  coil  is  wound. 

(4)  The  bichromate  battery. 
Procedure : 

(a)  Place  the  floating  magnet  at  the  east  or  west  end  of  a  lab- 
oratory table.  Connect  the  ends  of  the  coil  to  the  battery  by  means 
of  wires  2  or  3  m.  in  length.  Bring  up  the  coil,  holding  it  with  its 
axis  in  the  east  and  west  direction  (Fig.  251),  until  a  noticeable  deflec- 
tion of  the  needle  is  produced. 

N 


FIG.  251. 

(£>)  Leaving  the  coil  stationary  in  the  position  selected,  insert  the 
bar  of  iron  from  the  end  furthest  from  the  needle  and  notice  the 
effect.  To  show  that  the  increased  deflection  is  not  due  to  perma- 
nent magnetization  of  the  bar,  withdraw  it  and  insert  it  again 


288 


THE  OUTLINES   OF  PHYSICS 


reversed  end  for  end.     If  iron  wires  are  used,  these  may  be  after- 
wards withdrawn  a  few  at  a  time  and  the  effect  noted. 

The  reason  for  the  increased  effect  is  that  the  number  of  lines  of 
force  encircling  the  coil  is  much  greater  when  the  iron  core  is  present. 
The  increased  strength  of  field  shows  itself  not  only  within  the  coil, 
but  throughout  the  surrounding  regions. 

252.  Magnetic  Saturation.  —  Iron  is  a  much  better  carrier 
of  lines  of  force  than  air,  permitting  of  the  formation  of 
about  3000  times  as  many  lines  for  a  given  magnetizing 
force.  It  is  not  capable,  however,  of  carrying  an  indefi- 
nitely great  number  of  lines.  As  the  magnetizing  force 
increases,  the  permeability  falls  off,  at  first  slowly,  then 
very  rapidly.  When  this  rapid  fall  of  permeability  occurs, 
we  say  that  the  iron  is  saturated. 

By  using  a  coil  of  wire  with  many  turns,  and  a  battery 
of  more  cells,  and  by  substituting  the  galvanometer  for 
the  floating  needle  in  Experiment  76,  the  saturation  of  an 
iron  bar  may  be  demonstrated.  The  effect  upon  the 
galvanometer  with  and  without  the  core  is  noted,  with 
constantly  increasing  currents.  At  first  these  bear  a 

nearly  constant  ratio,  but  as 
saturation  begins,  the  deflec- 
tion with  the  core  does  not 
increase  so  rapidly.  The  de- 
flections obtained  when  the 
core  is  removed,  measure  the 
magnetizing  forces.  Those  ob- 
tained when  the  core  is  in 
place  are  proportional  to  the 
magnetization  of  the  iron. 

The    results    thus    obtained, 

if   expressed   graphically,  would  give  a  curve   like   that 
shown  in   Fig.  252.      Deflections  without   the   core   are 


5000 


MAGNETIZING  FORCE    H 


FIG.  252. 


MAGNETISM 


289 


plotted  upon  a  scale  forty  times  as  large  as  those  obtained 
with  the  core.  The  magnetization  of  the  iron  rises  at 
first  nearly  in  proportion  to  the  magnetizing  force.  At 
the  point  s  it  bends  outwards.  Saturation  has  begun  to 
show  itself. 

253.  Magnetization  of  Other  Substances.  —  Nickel,  cobalt, 
manganese,    and    chromium    show    magnetic    properties 
similar   to  iron,  but   their   permeability  is  less.     Nickel, 
however,  is  sufficiently  susceptible  to  enable  one  to  pick 
a  considerable  piece  of  it  up  with  an  ordinary  horseshoe 
magnet.     Nearly  all  other  substances  are  capable  of  mag- 
netization only  in  slight  degrees.     Their  permeability,  in 
other  words,  is  very  nearly  unity.     Some  substances  have 
less  permeability  than  air.     They  are  said  to  be  diamag- 
netic.     When  placed  in  a  strong  magnetic  field,  they  tend 
to  set  themselves  at  right  angles  to  the  lines  of  force. 
Among   the   most   strongly   diamagnetic    substances    are 
bismuth  and   tellurium.      Oxygen,  both  in  the  form  of 
a  gas  and  a  liquid,  is  quite  strongly  magnetic. 

To  test  weakly  magnetic   or   diamagnetic   bodies,  the 
material   is   made   into  a  bar,  which  is  suspended   by  a 
delicate  fiber  of  quartz  or  silk 
in    a    strong    magnetic    field. 
The  field  employed  is  that  of 
an  electromagnet. 

254.  Electromagnets. — These 
are  magnets  in  which  the  field 
is  due  to  coils  of  wire  carrying 
strong  electric  currents.     The 
iron   core   serves   simply  as   a 

carrier   of   the  lines  of  force.  FIG.  253. 


290 


THE  OUTLINES   OF  PHYSICS 


It  is  preferably  of  soft  iron,  and  does  not  possess  apprecia- 
ble permanent  magnetism.  Figure  253  shows  a  favorite 
form.  There  is  a  bed  plate  of  iron  into  which  two 
upright  cylinders  of  iron  are  screwed.  Over  these  slip 
the  coils  of  wire.  Upon  the  cylindrical  cores  are  placed 
pole  pieces  ($,  .ZV),  also  of  soft  iron,  the  shape  of  which 
varies  with  the  experiment  to  be  performed. 

255.  *  EXPERIMENT  78.  —  Testing  Bodies  of  Low  Permeability. 

Apparatus  : 

(1)    An  electromagnet.      This   may  be   of  small   size,  like  that 

shown  in  Fig.  254,  the  coils   of  which   are 

only  5  cm.  long. 

(2)  The  bichromate  battery. 

(3)  Some  minute  bars  of  bismuth,  tellu- 
rium, zinc,  lead,  glass,  etc.,  not  more  than  1 
cm.  long,  and  -1  or  -2  cm.  in  diameter.     The 
metals  may  be  made  into  such  bars  by  melting 
in  a  crucible,  and  sucking  them  up  into  the 
bore  of  glass  tubes.     The  glass,  when  cold, 
may  be  broken  away. 

Procedure  : 

Hang  the  bars  in  succession  between  the  poles  of  the  electromagnet, 
using  as  a  suspension  as  fine  a  fiber  of  cocoon  silk  as  you  can  obtain. 
Note  in  each  case  whether  the  bar  tends  to  set  itself  along  the  lines 
of  force  or  perpendicular  to  them. 

Bismuth  and  tellurium  should  show  marked  diamagnetic  properties. 
The  others,  although  classed  as  diamagnetic,  more  frequently  are 
slightly  magnetic  from  the  presence  of  iron  as  an  impurity. 


FIG.  254. 


MEASUREMENT  OF  CURRENT 


291 


CHAPTER  XXIX 

THE  MEASUREMENT    OF    CURRENT,  ELECTROMOTIVE  FORCE 
AND  RESISTANCE 

256.  The  Galvanometer,  —  The  arrangement  described  in 
Chapter  XXVII,  where  the  coil  of  wire  surrounds  a  floating 
needle,  contains  all  the  essential  features  of  the  instrument 
known  as  the  galvanometer. 
This  instrument,  which  we  have 
already  used  in  certain  experi- 
ments in  Heat,  and  the  construc- 
tion of  which  is  described  in 
some  detail  in  Appendix  VI, 
consists  of  a  suspended  magnet 
which  is  placed  in  the  axis  of  a 
coil  of  wire,  and  is  therefore  de- 
flected from  its  north  and  south 
position  whenever  a  current 
flows  through  the  coil.  The 
coil  of  wire  may  consist  of  one 
or  many  turns,  according  to  the 
strength  of  the  current  to  be 
measured.  For  the  measure- 
ment of  large  currents,  the 
galvanometer  is  frequently  given 
the  form  shown  in  Fig.  255. 

T        ,,  .  f  •    i       •  FIG.  255. 

In    this    instrument,    which    is 

called  the  tangent  galvanometer,  because  the  tangent  of  the 

angle  through  which  the  needle  is  deflected  is  proportional 


292 


THE   OUTLINES   OF  PHYSICS 


to  the  current,  the  coil  is  of  considerable  size,  from  20  to 
100  cm.  in  diameter.  In  many  cases,  as  in  that  of  the  in- 
strument selected  for  illustration,  two  coils  are  used,  and 
the  needle  is  placed  midway  between  them  in  their  common 
axis.  The  needle  was  originally 
constructed  like  a  mariner's  com- 
pass, being  pivoted  upon  a  steel 
point,  and  its  deflection  was  read,  in 
the  same  way,  upon  a  divided  circle. 
In  modern  instruments  such  needles 
,S  have  given  way  to  magnets  which 
are  suspended  by  means  of  a  delicate 
fiber  of  unspun  silk  or  of  fused 
quartz.  These  magnets,  which  are  given  various  shapes, 
sometimes  that  of  an  elongated  horseshoe,  as  shown  in 
Fig.  256,  a,  or  of  a  disk  or  ring  as  shown  in  b  and  c  of 
that  figure,  or  of  a  couple  of  steel  strips  as  shown  in  d, 
bear  but  little  resemblance  to  a  needle  :  the  name,  how- 
ever, is  retained.  Instead  of  reading  the  deflections  of 
j  the  galvanometer  needle  upon  a  divided  circle, 
it  is  customary  to  attach  to  the  same  a  mirror, 
and  to  observe  the  movements  of  this  mirror  by 
means  of  a  telescope  and  scale. 


FIG.  256. 


IN-4-S' 


257.  Sensitive  Galvanometers.  —  In  galvanom- 
eters for  the  measurement  of  very  minute  cur- 
rents the  coil  contains  a  great  many  turns  of 
wire  and  is  of  small  diameter.  The  wire  is 
thus  brought  as  near  as  possible  to  the  needle. 
In  many  cases  two  needles  are  used.  These 
are  turned  north  pole  opposite  south  pole  as  in  Fig.  257. 
Such  an  arrangement  is  called  an  astatic  pair.  Each 
needle  is  placed  in  the  axis  of  a  coil,  or  of  a  pair  of  coils. 


FIG.  257. 


MEASUREMENT  OF  CURRENT 


293 


The  action  of  the  earth's  magnetism  upon  the  system  is 
very  small,  because  the  two  needles  oppose  each  other; 
the  currents  in  the  coil,  however,  flow  so  as  to  act  in  the 
same  direction  upon  both  needles.  Great  delicacy  is  thus 
obtained. 

By  means  of  the  galvanometer  numerous  important 
electrical  measurements  may  be  made,  and  a  great  number 
of  interesting  experiments  may  be  performed. 

258.    EXPERIMENT  79.  —  Fall  of  Potential  in  a  Homogeneous  Circuit. 

Apparatus  : 

(1)  The  sensitive  galvanometer  described  in  Appendix  VI. 

(2)  A  cell  of  bichromate  battery. 

(3)  Four  meters  of  fine  copper  wire  (No.  26  or  28). 

(4)  A  resistance  box  of  at  least  1000  ohms. 
Procedure  : 

(a)  Strip  the  wire  carefully  of  its  insulation.     Connect  one  end  to 
the  carbon  pole  of  the  cell,  and  stretch  the  wire  for  half  its  length 
along  a  laboratory  table,  thence  around  a  support,  and  back  to  the 
battery.     Attach  the  free  end  to  the  zinc  pole. 

(b)  Connect  the  resistance  box  in  series  with  the  galvanometer, 


GALVANOMETER 


FIG.  258. 


s_ ,  *-^ 

u 

FIG.  259. 


and  bring  wires  to  the  terminals  of  the  cell  as  in  Fig.  258.  Close  the 
circuit  and  observe  the  deflection.  If  the  deflection  is  too  large  and 
no  more  resistance  is  available,  shunt  the  galvanometer.  This  is 
done  by  connecting  a  wire  between  the  terminals  to  divert  a  portion 
of  the  current  from  the  coils  (Fig.  259).  The  shorter  and  thicker 
the  wire,  the  less  current  will  flow  through  the  galvanometer.  It- 
is  best  to  begin  with  a  fine  wire  of  considerable  length  and  to  shorten 


•1— 


294  THE  OUTLINES  OF  PHYSICS 

the  same  until  a  suitable  deflection  has  been  obtained.  Having  ad- 
justed the  shunt  as  above,  note  the  deflection. 

(c)  Detach  the  galvanometer  wire  from  the  cell  and  make  contact 
at  b  (in  the  middle  of  the  stretched  wire),  c  (at  three  fourths  the  dis- 
tance along  the  wire),  at  d  (seven  eighths  of  the  distance  from  a  to/), 
and  at  e  (fifteen  sixteenths  of  that  distance),  successively.  Note  the 

deflections  and  determine  the 
relation  between  the  deflection 
and  the  length  of  wire  included 
between  the  terminal  /and  the 
points  of  contact.  For  this  pur- 
pose, plot  a  curve  like  that 
shown  in  Fig.  260.  Ordinates 
are  lengths  of  wire  and  abscissas 

DEFLECTIONS  are    deflections.      If    the   work 

has  been  carefully  done  this 
curve  will  be  almost  a  straight 

line.  The  experiment  will  thus  serve  to  verify  the  statement  that  in  a 
homogeneous  circuit  (one  consisting  of  a  wire  of  uniform  diameter  and 
composed  of  the  same  metal  throughout)  the  fall  of  potential  is  every- 
where proportional  to  the  length  of  wire. 

259.  Resistance  and  Electromotive  Force.  —  The  resistance 
in  any  portion  of  a  circuit  is  measured  by  the  fall  of  poten- 
tial in  that  portion.    The  conception  of  current  leads  natu- 
rally to  the  idea  of  a  force  needed  to  drive  the  current 
through  the  resisting  portion.     It  is  usual,  therefore,  to 
speak  of  electromotive  force.      This  is   the   equivalent  of 
fall  of  potential,  although  the  terms  are  not  identical  in 
meaning  in  every  respect.     When  we  speak  of  the  electro- 
motive force  of  a  battery,  we  mean  its  power  of  producing 
current. 

260.  Ohm's  Law.  —  The  current  (7)  in  a  given  circuit 
is  directly  proportional  to  the  electromotive  force 

and  inversely  as  the  resistance  R.     Thus, 


MEASUREMENT  OF  CURRENT  295 

This  relation  is  known  as  Ohm's  law.  It  makes  it  pos- 
sible to  compute  the  current  in  any  circuit  in  which  elec- 
tromotive force  and  resistance  are  known,  or,  indeed,  to 
find  any  one  of  the  three  quantities,  J,  E,  and  R,  when 
the  other  two  are  given. 

261.  EXPERIMENT  80.  —  The  Resistance  of  a  Wire  is  inversely 
as  its  Cross-Section. 

Apparatus : 

The  apparatus  is  the  same  as  in  the  foregoing  determination, 
excepting  that  the  circuit  to  be  measured  contains  three  sizes  of 
copper  wire,  ab,  be,  and  cd,  BATTERY 

attached  to  each  other  as     , 1 1 — ^^ 

shown  in  Fig.  261.  v * 1  |  ,      ' 

Procedure: 

,      .  FIG.  261. 

(a)  Instead  ot  connect- 
ing the  wires  of  the  galvanometer  circuit  to  the  terminals  of  the 
battery,  as  in  the  preceding  determination,  fasten  their  ends  across 
the  meter  stick  at  a  distance  of  50  cm. 
apart,  and  allow  about  3  cm.  of  naked 
wire  to  extend  beyond  the  edge  of  the 
stick  as  shown  in  Fig.  262. 

(&)  Rub  the  three  pieces  of  copper 

wire  which  constitute  the  part  of  the  Fio.  262. 

circuit  to  be  tested  with  fine  sandpaper, 

and,  having  cleaned  the  ends  of  the  galvanometer  wires  in  the  same 
manner,  compare  the  fall  of  potential  through  50  cm.  of  the  three 
wires  in  question  by  means  of  the  deflection  produced  when  the 
terminals  of  the  galvanometer  circuit  are  brought  into  contact,  first 
with  the  piece  of  wire  ab,  then  with  be,  and  finally  with  cd.  Make  a 
series  of  at  least  ten  sets  of  readings,  and  average  the  deflections  for 
each  wire  separately.  The  deflections  indicate  the  fall  of  potential 
between  the  circuits  of  the  galvanometer,  and  this  fall  of  potential,  as 
has  been  shown  in  the  foregoing  article,  is  proportional  to  the  inter- 
vening resistance. 

(c)  Measure  the  diameters  of  the  three  pieces  of  wire,  ab,  be,  and 
cd,  with  the  micrometer  gauge,  and  compute  the  cross-section  of  each. 
Divide  the  average  deflection  obtained  by  contact  with  each  wire  by 


296  THE  OUTLINES   OF  PHYSICS 

its  cross-section.  The  result  should  be  the  same  in  the  three  cases. 
The  variations  in  the  three  results  will  be  due :  First,  to  errors  of 
observation.  Secondly,  to  failure  to  make  good  contact  with  the 
galvanometer  terminals ;  this  is  an  avoidable  error,  since  it  depends 
on  the  proper  cleaning  of  the  surfaces.  Thirdly,  to  differences  in  the 
quality  of  the  copper  of  which  the  three  wires  are  constructed. 

262.  EXPERIMENT  81.  —  Specific  Resistance.  —  In  comparing  the 
resistance  offered  by  different  metals  to  the  passage  of  the  current, 
very  great  differences  are  found.     It  is  customary  to  express  resist- 
ances in  terms  of  the  resistance  of  a  block  of  the  substance  in  ques- 
tion, 1  cm.2  in  cross-section,  and  1  cm.  long.     Resistance  expressed 
in  this  way  is  called  specific  resistance.    It  is,  in  general,  impracticable 
to  measure  the  resistance  of  so  thick  and  so  short  a  piece  of  metal ; 
but,  since  resistance  is  always   proportional  to  the  length    and  in- 
versely proportional  to  the  cross-section,  one  can  measure  the  resist- 
ance of  any  convenient  sample,  and  compute  from  that  the  specific 
resistance  of  the  substance.     By  means  of  the  method  of  the  fall  of 
potential  which  has  been  employed  in  the  two  foregoing  determina- 
tions, it  is  easy  to  compare  the  resistance  of  various  metals.      The 
practical  unit  of  resistance  is  called  an  ohm ;   it  is  the  resistance  of  a 
column  of  mercury  106-3  cm.  long,  and  containing  14-4521  g.  of  mercury. 
This  gives  a  cross-section  of  1  mm.     Mercury  is  selected  in  defining 
this  unit  instead  of  any  solid  metal,  because,  being  a  liquid,  it  has  no 
structure. 

263.  EXPERIMENT  82.  —  Comparison  of  the  Resistance  of  Various 
Metals. 

Apparatus : 

The  apparatus  is  the  same  as  in  the  foregoing  experiments  except- 
ing that  the  circuit  is  made  up  of  pieces  of  wire,  each  more  than 
50  cm.  long,  consisting  of  copper,  iron,  brass,  German  silver,  and 
platinum.  These  are  to  be  joined  end  for  end  by  soldering.  The 
last  of  the  series,  namely,  the  platinum,  is  connected  with  the  battery 
cell  by  means  of  a  copper  wire.  It  is  not  necessary  that  the  diameters 
be  identical,  but  it  is  convenient  to  deal  with  wires  of  about  the  same 
size,  and  possessing  a  diameter  of  approximately  0-05  cm. 

Procedure  : 

(a)  Having  cleaned  the  various  wires  with  fine  sandpaper,  stretch 


MEASUREMENT  OF  CURRENT  297 

them  out  upon  a  laboratory  table  between  two  supports  as  shown  in 
Fig.  263. 

(&)  Make  contact  successively  with  the  various  metals,  using  the 
galvanometer  terminals  mounted  as  in  the  foregoing  determination ; 
note  the  deflection  obtained  in  each  case,  and  make  a  series  of  at  least 
ten  readings  for  each  wire. 

COPPER  IRON  BRASS        GERMAN  SILVER     PLATINUM 

1 1 h 


GALVANOMETER 


FIG.  263. 

(c)  Measure  the  diameters  of  the  various  wires  with  the  microme- 
ter gauge,  and  compute  their  cross-sections.     Multiply  the  average 
deflection  in  each  case  by  the  cross-section  of  the  wire  to  which  it 
belongs.      The  results  will  be  the  relative  resistances.     The  set  of 
values  thus  obtained,  divided  by  the  relative  resistance,  of  copper,  will 
give  each  resistance  in  terms  of  that  of  copper.     Now,  the  specific 
resistance  of  copper  is  1-7  millionths  of  an  ohm.     If  we  multiply  the 
foregoing  set  of  values  by  this  quantity,  we  shall  obtain  the  values 
for  the  specific  resistance  of  the  various  metals. 

(d)  Compare  your  results  with  the   following  table   of  specific 
resistances : 

TABLE  OF  SPECIFIC  RESISTANCES  IN  MILLIONTHS  OF  AN  OHM. 


Aluminium 3'0 

Brass 6-9 

Copper 1-7 

Gold 2-1 

German  silver  23-6 


Iron 11-1 

Lead 19-6 

Platinum 13'5 

Silver    .  1-5 


On  account  of  varying  differences  of  hardness  and  temper,  samples 
of  the  same  metals  show  a  considerable  difference  in  the  resistance. 

264.  The  Wheatstone's  Bridge.  —  Another  and  more  accu- 
rate method  of  measuring  resistance  is  that  of  the  Wheat- 
stone's  bridge.  This  method  depends  upon  the  principle, 


298  THE  OUTLINES   OF  PHYSICS 

already  demonstrated  in  foregoing  articles,  that  the  fall  of 
potential  along  a  circuit  is  everywhere  proportional  to  the 
resistance.  If,  therefore,  we  have  a  divided  circuit,  con- 
sisting of  two  branches  abc  and  acd)  (Fig.  264)  of  any 


resistance  whatever,  and  if  we  select  points  b  and  d  so 
that  the  resistance  on  both  sides  of  them  in  each  branch 
are  in  the  proportion 

ab  :  be  : :  ad  :  dc, 

then  the  fall  of  potential  through  ab  will  be  the  same  as 
that  through  ad,  and  there  will  be  no  difference  of  poten- 
tial between  b  and  d.  A  galvanometer  inserted  between 
these  points  will  show  no  flow  of  current,  however  large  a 
current  may  be  flowing  through  the  divided  circuit.  If 
three  of  the  four  resistances  above  mentioned  are  known, 
the  fourth  one  can  be  computed  by  means  of  the  above 
proportion.  This  arrangement  is  called  a  WJieatstone 's 
bridge. 

265.  Resistance  Boxes.  —  For  convenience  in  the  com- 
parison of  resistances,  it  is  customary  to  place  a  set  of  coils 
of  wire,  previously  adjusted  to  measure  an  exact  number 
of  ohms  each,  within  a  box.  The  terminals  of  these  coils 
are  attached  to  a  row  of  brass  blocks  fastened  to  the  top 
of  the  box  as  shown  in  Fig.  265,  and  these  blocks  may  be 
connected  by  the  insertion  of  plugs.  The  general  appear- 
ance of  such  a  box  is  shown  in  Fig.  266.  The  values  of 


MEASUREMENT  OF  CURRENT 


299 


the.  coils  are  like  those  of  a  set  of  weights,  i.e.  1,  2,  2,  5, 
10,  20,  20,  50,  100",  200,  200,  500,  etc. 


T  1 

TT 


FIG.  265. 


FIG.  266. 


266.  EXPERIMENT  83.  —  Measurement  of  the  Resistance  of  a  Coil 
of  Copper  Wire  with  the  Wheatstone's  Bridge. 

Apparatus : 

(1)  A  piece  of  iron  or  German  silver  wire  1  m.  long ;  a  meter  stick. 

(2)  The  resistance  box  used  in  the  foregoing  determination. 

(3)  A  coil  or  spool  of  fine  copper  wire,  the  resistance  of  which  is  to 
be  measured. 

(4)  A  galvanometer. 
Procedure : 

(a)  Stretch  the  piece  of  iron  or  German  silver  wire  between  two 
binding  screws,  adjusting  it  so  that  the  length  is  as  nearly  as  possible 
1  m.  Lay  the  meter  stick  alongside  the  wire  with  its  ends  corre- 


sponding to  the  ends  of  the  former.  Solder  to  the  posts  short  pieces 
of  copper  wire.  One  of  these  leads  to  the  resistance  box,  the  other 
to  the  coil  of  wire,  the  resistance  of  which  is  to  be  determined.  Con- 


300  THE  OUTLINES   OF  PHYSICS 

nect  the  other  terminal  of  the  resistance  box  and  the  other  end  of 
the  spool  of  copper  wire  by  means  of  a  heavy  copper  wire  as  shown  in 
Fig.  267. 

Attach  one  terminal  of  the  galvanometer  at  a  and  hold  a  wire 
connected  with  the  other  terminal  in  the  hand ;  connect  wires  from 
the  terminals  of  the  cell  of  bichromate  battery  to  the  binding  posts 
at  the  ends  of  the  stretched  wire.  This  arrangement  is  a  simple  form 
of  what  is  known  as  the  slide-wire  bridge. 

(6)  Whatever  be  the  resistance  of  the  coil  of  wire  to  be  tested, 
which  should  however  for  convenience  be  of  about  the  same  as  the 
resistance  of  the  box  used  in  the  other  branch  of  the  bridge,  it  will 
be  possible  to  find  a  point  upon  the  stretched  wire  at  which  the  free 
terminal  of  the  galvanometer  may  be  brought  into  contact  with  the 
wire  without  producing  a  deflection.  Determine  this  point  as  nearly 
as  possible  and  note  its  position  upon  the  wire.  Call  this  point  d. 

From  the  principle  of  the  Wheatstone's  bridge  above  stated,  we 
have 

ab  :  be  : :  ad  :  dc. 

Since  the  resistance  ad  and  dc  are  proportional  to  the  intervening 
lengths  of  wire,  we  can  compute  the  resistance  of  the  spool  of  wire  to 
be  tested  in  terms  of  that  of  the  coils  within  the  resistance  box. 


267.    EXPERIMENT  84.  —Influence  of  Temperature  upon  Resistance. 

Apparatus : 

(1)  The  slide-wire  bridge  described  in  Art.  266. 

(2)  Wires  of  iron  or  platinum  and  German  silver ;  also  a  carbon 
rod. 

(3)  Two  jars  and  a  U-shaped  tube.     (See  Fig.  268.)  ^f- 
Procedure  : 

(a)  Substitute  for  the  spool  of  copper  wire  used  in  Experiment  83, 
a  piece  of  fine  iron  or  platinum  wire  wound  upon  a  glass  tube ;  this 
wire  should  be  uninsulated. 

(&)  Balance  the  Wheatstone's  bridge  and  heat  the  coil  of  iron  or 
platinum  wire  with '  a  Bunsen  burner.  Note  that  the  galvanometer 
begins  to  show  deflection,  which  increases  as  the  temperature  of  the 
wire  rises.  Note  that  the  direction  of  this  deflection  is  such  as  to 
indicate  that  the  resistance  of  the  wire  has  been  increased  by  heating. 

(c)  Repeat  the  above  experiments,  using  a  piece  of  German  silver 


MEASUREMENT  OF  CURRENT  301 

wire,  and  note  that  the  effect  of  temperature  in  this  case  is  much 
smaller. 

(d)  Repeat  the  experiment,  using  a  slender  rod  of  carbon  ;  a  quarter 
inch  arc  light  carbon  will  answer  this  purpose,  or  even  the  graphite  of 
an  ordinary  lead  pencil.     Note  that  the  effect  of  temperature  upon 
the  carbon  is  opposite  to  tnat  in  case  of  the  metals,  namely,  that  the 
influence  of  temperature  is  to  decrease  the  resistance. 

(e)  Repeat  the  experiment,  using  a  column  of  acidulated -water. 

This  column  of    liquid    may  be   obtained  by  _  _ ^ 

filling  a  siphon  tube  between  two  jars.     (See 

Fig.  268.)     Upon  warming  this  tube  of  liquid      fjjn 

with  the  flame,  it  will  be  found  that  its  resist-     ^^^   _, 

ance  is  likewise  diminished  by  heating.     The 

facts   established   by   means   of    this   experiment  may  be  stated  as 

follows : 

(1)  The  resistance  of  metals  is  increased  by  heating.    The  increase 
in  the  case  of  pure  metals  amounts  to  about  40  per  cent  for  100°  rise 
of  temperature. 

(2)  The  influence  of  temperature  upon  the  resistance  of  alloys  is 
much  less  than  in  the. case  of  pure  metals. 

(3)  The  resistance  of  carbon  is  slightly  diminished  by  rise  of  tem- 
perature. 

(4)  The  resistance  of  all  electrolytes  falls  as  the  temperature  rises. 


302  THE  OUTLINES   OF  PHYSICS 


CHAPTER   XXX 
THE  HEATING  EFFECT  OF  THE  ELECTRIC  CURRENT 

268.  Transformation  of  Energy  by  Means  of  the  Current. 
—  The  electric  current,  as  has  already  been  shown,  con- 
sists in  the  equalization  of  the  differences  of  potential  in 
different  parts  of  the  electric  circuit.     These  differences 
of   potential  have  been  produced  by  the  expenditure  of 
energy.     In  the  continuous  discharge  which  constitutes 
the  current  this  energy  is  liberated  again  in  the  form  of 
heat.      The  heat   thus   produced   shows   itself   wherever 
resistance  is  offered  to  the  passage  of  the  current  and  in 
proportion  to  that  resistance. 

269.  Joule's  Law.  —  The  amount  of  heat  energy  developed 
in  the  circuit  is  proportional  to  the  product  of  the  square 
of  the  current  into  the  resistance.     This  is  known  as  Joule's 
law. 

The  development  of  heat  at  points  of   high  resistance 
may  be  demonstrated  as  follows : 

270.  EXPERIMENT   85.  —  The  Heating  of  Platinum  Wire  by  the 
Current. 

Apparatus  : 

(1)  The  plunge  battery;  a  short  piece  of  fine  platinum  wire  about 
0-025  cm.  in  diameter  (No.  30). 

(2)  A  similar  piece  of  copper  wire  as  nearly  as  possible  of  the 
same  diameter ;  also  2  or  3  m.  of  larger  copper  wire. 

Procedure : 

(a)  Stretch   the  platinum  wire   between   two  wooden  blocks,  as 


HEATING  EFFECT  OF  THE  ELECTRIC  CURRENT       303 


shown  in  Fig.  269.     Cut  the  larger  wire  in  two  equal  parts  and  con- 
nect with  the  terminals  of  the  battery. 

(&)  Take  the  free  ends  of  these  wires  in  the  hands,  and  having 
scraped  them  clean  apply  them  to  the  ends  of  the  stretched  platinum 
wire.     Make  contact  between  the  plati- 
num and  the  copper  wire  with  the  two 
terminals,  bringing    these    successively 
nearer  and  nearer  together,  and  note  the 
effect.     As  the  strip  of  platinum  wire  in  pIG-  269. 

the  circuit  becomes  shorter,  its  tempera- 
ture will  rise  until  it  becomes  red  hot  and  finally  white  hot.     The 
platinum  wire  may  even  be  melted  by  sufficiently  reducing  the  dis- 
tance between,  the  copper  terminals. 

(c)  Repeat,  using  the  fine  copper  wire  instead  of  the  platinum. 
Note  that  the  heating  effect  is  much  less. 

(d)  Join  the  copper  and  platinum  wires  end  to  end,  and  stretch 
between  the  blocks  with  the  junction  midway.     Repeat  the  experi- 
ment, moving  the  contact  wires  inward  from  the  blocks  so  as  to  in- 
clude always  equal  lengths  of  copper  and  platinum  between  them. 
Note  that,  although  the  same  current  flows  in 

both  wires,  the  platinum  becomes  much  hotter 
than  the  copper.  The  resistance,  length  for 
length,  of  the  platinum  wire  is  more  than  nine 
times  as  great  as  that  of  the  copper,  and  it  is  in 
this  portion  of  higher  resistance  that  the  heat  is 
chiefly  developed. 

271.  The  Glow  Lamp.  —  Another  ma- 
terial which  offers  high  resistance  to  the 
current  is  carbon,  and  since  this  is  capa- 
ble of  being  heated  to  very  high  tempera- 
tures without  fusion,  it  is  used  for  the 
purpose  of  obtaining  light  by  the  expen- 
diture of  electrical  energy.  A  narrow 
filament  of  carbon  is  inclosed  in  a  glass  bulb  (Fig.  270) 
from  which  the  air  has  been  exhausted.  The  removal  of 
the  air  serves  a  double  purpose :  on  the  one  hand  it  pre- 


FIG.  270. 


304 


THE  OUTLINES   OF  PHYSICS 


vents  oxidation  of  the  carbon,  which  would  speedily 
destroy  it,  and  on  the  other  it  reduces  the  loss  of  heat 
by  convection.  Current  is  conveyed  to  this  filament  by 
means  of  platinum  wires  sealed  in  the  glass.  Such  an 
arrangement  is  called  a  glow  lamp  or  an  incandescent  lamp 
(Fig.  270). 

The  lamps  generally  used  in  artificial  lighting  require 
the  use  of  a  source  of  electromotive  force  much  higher 
than  those  described  in  this  book.  It  is  possible,  how- 
ever, to  obtain  small  lamps  which  may  be  brought  to 
incandescence  by  the  use  of  a  very  few  cells  of  battery, 
or  even  of  a  single  cell.  The  lamps  used  in  the  lighting 
of  houses  require  a  difference  of  potential  at  their  ter- 
minals of  50  to  150  volts.  The  currents  employed  range 
from  J  an  ampere  to  1J  amperes.  The  source  of  current 
is  generally  a  dynamo  machine. 


272.   EXPERIMENT  86.  —  Determination   of  the   Power   expended 
in  a  Glow  Lamp. 

Apparatus : 

(1)  A  miniature  or  "pea"  lamp  of  5  or  6  volts. 

(2)  A  small  calorimeter  containing  about  250  cm.2  of  water. 

(3)  A  good  thermometer. 

(4)  A  timepiece. 
Procedure : 

(«)  Solder  to  the  terminals  of 
the  lamp  two  copper  wires.  Slip 
these  through  a  glass  tube  and  draw 
the  latter  up  snugly  to  the  base 
of  the  lamp.  Fill  the  tube  with 
paraffin,  taking  care  that  the  wires 
do  not  become  crossed,  and  that  the 
wires  from  the  point  where  they 
leave  the  lamp  to  the  further  end 
FIG.  271.  of  the  tube  are  well  embedded  in 


HEATING  EFFECT  OF  THE  ELECTRIC  CURRENT      305 

the  paraffin.  Mount  the  lamp  within  the  calorimeter  as  shown  in 
Fig.  271.  Weigh  out  200  g.  of  water,  and  pour  the  same  into  the 
calorimeter. 

(6)  Connect  the  lamp  in  circuit  with  the  battery,  using  a  number 
of  cells  sufficient  to  bring  it  to  incandescence,  but  not  enough  to 
imperil  the  filament.1  Leave  the  circuit  open. 

(c)  Note  th%temperature  of  the  water. 

(d)  At  a  time  accurately  noted,  close  the  circuit.     Stir  the  water 
and  watch  the  thermometer  until  the  temperature  has  risen  about 
10°.    Then  break  circuit,  noting  the  time.    Stir  the  water  in  calorime- 
ter and  read  the  thermometer. 

(e)  Compute  the  gram  calories  of  heat  produced  by  the  lamp  in 
one  second. 

(/)  Compute  the  power  necessary  in  "horse  power"  (one  horse 
power  if  converted  into  heat  will  produce  179-3  calories  of  heat  per 
second). 

273.  The  Arc  Light.  —  When  an  electric  circuit  is  inter- 
rupted, great  heat  is  developed  at  the  point  of  interruption 
during  the  short  interval  of  time  when  bad  contact  exists 
between  the  terminals,  which  are  being  withdrawn  from 
one  another.  The  terminals  become  heated,  and  as  they 
are  withdrawn  the  air  lying  between  them  also  becomes 
intensely  hot.  .Now  a  hot  gas  is  a  good  conductor  of 
electricity,  and  if  the  difference  of  potential  between  the 
terminals  is  at  least  25  volts,  a  sufficient  current  will  flow 
to  keep  the  gas  permanently  hot.  This  flow  of  current 
across  a  heated  air  gap  is  called  an  electric  arc.  The 
temperatures  developed  in  such  cases  are  very  high,  and 
if  metals  be  employed  as  terminals  they  are  rapidly  vola- 
tilized. By  substituting  rods  of  carbon  for  the  metallic 
conductors,  we  may,  however,  maintain  the  arc  between 
them  for  a  long  time.  Carbon  is  the  only  conductor 

1  For  a  lamp  marked  "  5  volts  "  four  cells  of  bichromate  battery  may 
be  used. 


306 


THE  OUTLINES   OF  PHYSICS 


which  will  sustain  the  temperatures  thus  created  without 
very  rapid  destruction. 

The  carbon  terminals  where  the  current  passes  from 
the  air  gap  to  the  solid  conductors  become  heated  to 
brilliant  incandescence,  and  the  light  which  they  give 
off  is  the  most  powerful  of  all 
artificial  lights.  It  is  employed 
in  the  arc  lamp. 

Figure  272  gives  a  picture  of 
the  electric  arc  between  carbon 
terminals.  It  is  taken  from  a 
photograph.  It  will  be  seen 
that  the  most  brilliant  portion 
is  the  surface  of  the  upper  car- 
bon. This  is  the  positive  ter- 
minal, that  from  which  the 
current  flows  into  the  arc.  The 
end  of  the  positive  carbon  is 
eaten  away  so  as  to  form  a  con- 
cave region  called  the  crater,  and  it  is  the  crater  which 
emits  the  most  intense  light.  The  negative  carbon  is  also 
incandescent,  but  does  not  reach  so  high  a  temperature. 
The  light  which  it  gives  off  is  comparatively  feeble.  The 
temperature  of  the  crater,  according  to  Rossetti,  is 
3900°  C. ;  that  of  the  negative  carbon,  2500°  C. 


FIG.  272. 


ELECTROLYSIS  307 


CHAPTER   XXXI 
ELECTROLYSIS 

274.  The  Law  of  Electrolysis.  —  The  chemical  effect  of 
the  electric  current  consists  in  breaking  up  liquids  through 
which  it  passes  into  two  parts,  the  metal  and  the  acid- 
radical  with  which  this  is  combined  to  form  a  salt.     Cop- 
per sulphate   (CuSO4),  for  example,  is  decomposed  into 
copper  (Cu)  and  the  acid  radical  (SO4).     In  order  that 
a   compound   may  be   thus    decomposed,  it   is   necessary 
that  it  be  a  conductor  of  electricity.     Substances  which 
thus  conduct  the  current,  and  in  conducting  it  are  broken 
up,  are  called  electrolytes.     Nearly  all  liquid   conductors 
are  electrolytes ;  the  only  exceptions  being  molten  metals. 
These  are  not  chemical  compounds,  and  consequently  are 
not  capable  of  electrolysis. 

275.  Ions.  —  The    parts    into    which    an    electrolyte   is 
broken  up  by  the  action  of  the  current  are  called  its  ions  ; 
thus  in  the  case  of  silver  nitrate  the  ions  are  Ag  and  NO3. 
These  ions  are  separated  by  the  action  of  the  current,  and 
the  metallic  atoms  move  in  the  direction  in  which  the 
current  is  flowing  arid  are   deposited  upon  the  terminal 
at  which  the  current  leaves  the  electrolytic  cell.     (See 
Fig.  273.)     These  metallic   ions,  which  travel  with  the 
current,  are  called  Jcations ;  the  other  ions,  anions,  move 
towards  the  other  terminal  of  the  cell,  where  they  are  set 
free.    •  These    consist  of   the  group  of   atoms   known  in 
Chemistry  as   the    acid   radical.      Since  an  acid    radical 
is   an   incomplete    and    chemically   unsatisfied    group,   it 


308  THE  OUTLINES   OF  PHYSICS 

immediately  attacks  the  material  of  the  terminal,  or  the 
solution  itself,  and  enters  into  combination.  The  terminals 
of  the  electrolytic  cell  are  called  electrodes.  The  one  at 


SO*  set  free  |  x    Cu  deposited 

atthisTerminaNx       LL^^^  I  /'   at  this  Terminal 


Anode'  x  Kathode 

FIG.  273. 

which  the  current  enters  the  solution,  and  where  the 
anions  are  liberated,  is  called  the  anode.  The  one  where 
the  current  leaves  the  cell,  and  where  the  metallic  iron 
is  deposited,  is  called  the  kathode. 

It  will  be  seen  from  the  above  that  the  chemical  reactions 
which  result  from  the  passage  of  a  current  through  an 
electrolyte,  are  generally  twofold.  We  have,  first,  the 
decomposition  of  the  electrolyte  into  its  ions.  If  a  solu- 
tion of  copper  sulphate  be  subjected  to  electrolysis  the 
copper  will  be  deposited  upon  the  kathode,  and  the  anion 
(SO4)  will  be  set  free  at  the  surface  of  the  anode.  The 
SO4  anion  immediately  attacks  the  water  in  which  the 
sulphate  of  copper  has  been  dissolved,  combining  with 
the  hydrogen  atoms  to  form  free  sulphuric  acid  (H2SO4), 
and  liberating  oxygen  gas  which  appears  in  bubbles  at  the 
surface  of  the  anode.  If  the  anode  consists  of  copper,  the 
SO4  attacks  it,  forming  copper  sulphate  (CuSO4);  if  it 
consists  of  platinum  or  of  carbon,  which  will  not  unite  with 
the  acid  radical,  the  free  acid  remains  in  the  solution  un- 
combined. 

The  foregoing  statement  concerning  electrolysis  may  be 
readily  illustrated  by  means  of  the  following  experiments : 


ELECTROLYSIS 


309 


276.    EXPERIMENT  87.  —  Electrolysis  of  Sulphate  of  Copper. 

Apparatus : 

(1)  The  bichromate  battery  previously  described. 

(2)  A  beaker ;  two  strips  of  platinum  foil ;  some  small  copper  wire. 

(3)  About  100  g.  of  sulphate  of  copper. 
Procedure : 

(a)  Dissolve  the  sulphate  of  copper  in  water  and  nearly  fill  the 
beaker  with  the  solution.    To  the  terminals  of  the  battery,  which  should 
consist  of  three  or  four  cells,  attach  pieces  of  copper  wire  each  about 
1  cm.  in  length.     To  the  free  ends  of  these, 
after  removing  the  insulation  for  a  distance 
of  4  or  5  cm.,  attach  the  strips  of  platinum 
foil.     For  this  purpose  the  latter  is  cut,  as 
shown  in  Fig.  274,  and  the  flaps  thus  pro- 
duced are  rolled  snugly  around  the  naked 
wire,  which  should  have  been  previously  well 
scraped.     The  wire  should  then  be  bent  at 
right  angles  to  itself,  as  shown  in  the  figure. 

(6)  Dip  the  two  pieces  of  platinum  foil 
thus  attached  into  the  electrolyte.  Note 
that  at  one  electrode  gas  rises,  and  that  this 
occurs  at  the  surface  of  the  foil  which  is  con- 
nected with  the  carbon  pole  of  the  battery. 
This  means  that  the  SO*  radical  has  moved  against  the  current,  and 
that,  at  the  surface  of  the  foil,  free  sulphuric  acid  has  been  formed 
and  oxygen  set  free  as  explained  in  previous  article.  The  kathode, 
where  no  gas  appears,  will  be  found,  if  removed  after  the  current  has 
been  passing  for  a  few  minutes,  to  be  coated  red  with  copper. 

(c)  Reverse  the  direction  of  the  current  by  exchanging  the  wires 
at  the  terminals  of  the  battery.  Note  that  at  first  no  gas  escapes  at 
either  terminal ;  but  that,  after  a  period  about  as  great  as  that  previ- 
ously has  elapsed,  gas  begins  to  appear  at  the  electrode  upon  which 
copper  had  been  deposited  and  which  has  now  become  the  anode. 
Remove  the  strips  of  platinum  foil  from  the  beaker,  and  note  that  the 
one  which  had  been  plated  has  lost  its  coating  of  copper  altogether, 
and  that  the  other  strip  is  now  copper  plated.  By  means  of  this  ex- 
periment, we  verify  the  statement  that  the  copper  ion  is  carried  in  the 
direction  in  which  the  current  flows  and  is  deposited  upon  the  kathode. 
The  evidence  with  reference  to  the  SO*  ion  is  not  so  direct.  The  fact 


FIG.  274. 


310  THE  OUTLINES   OF  PHYSICS 

that  free  acid  is  produced  in  the  neighborhood  of  the  anode,  when 
electrolysis  occurs,  can  be  more  directly  shown  by  means  of  the  follow- 
ing experiment : 

277.    EXPERIMENT  88.  —  Electrolysis  of  Sodium  Sulphate. 
Apparatus  : 

(1)  A  U-shaped  tube  of  the  form  shown  in  Fig.  275. 

(2)  The  platinum  electrodes  described  in  the  foregoing"  experiment. 

(3)  The  bichromate  battery. 

(4)  About  100  g.  of  the  neutral  sulphate  sodium  (Na2SO4) ;  also 
some  neutral  solution  of  litmus. 

Procedure : 

(a)  Dissolve  as  much  of  the  sodium  sulphate  as  will  be  readily 
taken  up  in  water,  and  add  a  sufficient  amount  of  the  litmus  solution 
to  color  the  liquid  a  rich  purple.  Fill  the 
tube  with  this  solution  and  insert  the  plati- 
num electrodes,  which  should  dip  well  be- 
neath the  surface. 

(5)  Connect  with  the  battery  and  note 
that  gas  is  liberated  from  both  electrodes ; 
also  that  the  solution  in  the  neighborhood 
of  the  anode  rapidly  changes  to  a  red  color, 
while  the  bluish  cast  of  the  solution  in 
the  neighborhood  of  the  kathode  increases. 
pIG  275  The  reddening  of  the  solution  in  the  neigh- 

borhood of  the  anode  is  indicative  of  the 

presence  there  of  free  acid,  a  point  which  it  is  one  of  the  purposes  of 
this  experiment  to  establish.  This  fact  may  readily  be  verified  by 
pouring  a  few  drops  of  the  litmus  solution  in  a  test  tube,  or  beaker, 
and  adding  a  drop  of  dilute  sulphuric  acid.  The  change  of  color  thus 
produced  will  be  seen  to  correspond  with  that  which  is  going  on 
within  the  electrolytic  cell.  A  drop  of  ammonium  added  to  the  litmus 
solution  will  likewise  be  found  to  intensify  its  blueness  in  a  manner 
corresponding  to  that  which  occurs  in  the  region  of  the  kathode. 

The  gases  generated  at  the  electrodes  in  this  experiment  are,  re- 
spectively, hydrogen  at  the  kathode  and  oxygen  at  the  anode.  The 
hydrogen  is  produced  by  the  combination  of  the  metallic  sodium,  set 
free  at  the  kathode  with  the  water  thus  : 

2  Na  +  2  H2O  =  2  NallO  +  2  H. 


ELECTR  OL  Y8IS  311 

At  the  anode  the  reaction  is  similar  to  that  which  has  already  been 
described,  viz. : 

SO4  +  H2O  =  H2SO4  +  O. 

278.  Voltameters.  —  The  quantity  of  metal  deposited  by  a 
current  is  proportional  to  the  strength  of  the  current  and  to 
the  time  it  flows.     This  law,  which  is  known  as  Faraday's 
law,  makes  it  possible  to  measure  the  quantity  of  electricity 
which  has  flowed  in  the  circuit.    By  dividing  this  quantity 
by  the  time,  we  obtain  the  average  strength  of  the  current. 
An  instrument  for  measuring  current  in  this  way  is  called 
a  voltameter. 

279.  The  Water  Voltameter.  —  An  instrument  designed 
for  the  measurement  of  current,  by  means  of  the  amount  of 
water  which  it  decomposes,  is  called  a  water  voltameter. 
In  the  decomposition  of  water  by  the  current,  hydrogen 
plays  the  part  of  a  metal,  and  oxygen 

that  of  the  acid  radical.  If,  therefore, 
two  platinum  electrodes,  like  those 
described  in  the  foregoing  experi- 
ments, be  inserted  in  a  dish  of  water, 
which  should  be  slightly  acidulated 
to  increase  its  conductivity,  and  if 
inverted  tubes,  closed  at  one  end  and 
filled  with  water,  be  placed  over  each 

*Gi_~ 

electrode,  as  shown  in  Fig.  276,  the 
current  sent  through  the  cell  will  liberate  hydrogen  gas 
at  the  surface  of  the  kathode,  which  will  rise  and  displace 
the  water  in  the  tube  placed  over  that  electrode,  while 
oxygen  will  similarly  be  collected  in  the  other  tube. 
The  volume  of  hydrogen  thus  produced  will  be  twice  as 
great  as  that  of  the  oxygen,  and  each  of  them  will  be 
proportional  to  the  time  and  to  the  average  strength  of 


312 


THE  OUTLINES   OF  PHYSICS 


the  current.  If  we  know  how  many  cubic  centimeters  of 
hydrogen  a  unit  of  current  is  capable  of  producing  in  one 
second  of  time,  we  can  tell,  from  the  volume  of  hydrogen 
produced  in  the  water  voltameter  in  a  given  time,  how 
strong  the  current  has  been.  The  water  voltameter  does 
not  give  accurate  results,  excepting  when  very  great  pre- 
cautions are  taken,  on  account  of  the  absorption  of  the 
gas  by  the  liquid  within  which  they  are  generated,  and 
the  occlusion,  especially  of  hydrogen,  at  the  surface  of  the 
platinum  electrode. 

Two  forms  of  voltameters,  with  which  it  is  possible  to 
obtain  much  better  results,  are  the  copper  voltameter  and 
the  silver  voltameter. 

280.  EXPERIMENT  89.  —  The  Measurement  of  Current  by  Means  of 
a  Copper  Voltameter. 

Apparatus : 

(1)  A  copper  voltameter.     The  form  of  voltameter,  by  means  of 
which  an  accurate  result  may  most  easily  be  obtained,  is  constructed 
as  follows :    Take  four  pieces  of  naked  copper  wire,  size  No.  12.    Two 
of  these  pieces  should  be  1  m.  long,  and  two  of  them  \  m.  long,  each. 
Clean  the  wire  with  sandpaper  and  make  it  up  into  four  spiral  coils, 
the  long  piece  into  coils  about  8  cm.  in  diameter,  and  the  short  pieces 
into  coils  with  a  diameter  of  4  cm.  each.     Pass  each  coil  through  the 
flame  of  the  Bunsen  burner  to  remove  the  oil  due  to  the  hand,  and 
plunge  it  into  a  dilute  solution  of  sulphuric  acid  and  then  into  water. 
Mount  the  coils  thus  prepared  as  shown  in  Fig.  277. 

(2)  The  bichromate  battery  previously  mentioned. 


FIG.  277. 


ELECTROLYSIS  313 

(3)  Two  beakers,  large  enough  to  contain  the  coils,  when  mounted 
as  shown  in  the  figure,  and  a  sufficient  quantity  of  the  solution  of 
sulphate  of  copper  (density  between  I'lO  and  1-18)  to  immerse  the  coils. 

Procedure : 

(a)  Weigh  all  four  coils  as  carefully  as  possible ;  then  mount  them 
as  described,  connect  them  with  wires  so  that  when  the  current  flows 
it  will  pass  in  each  case  from  a  large  to  a  small  coil,  leaving  the 
circuit  open  at  one  terminal  of  the  battery.  Fill  the  beakers  with 
the  solution  until  the  coils  are  entirely  submerged.  Close  the  circuit 
at  a  time  carefully  noted  by  means  of  a  watch  or  other  timepiece. 
Allow  the  current  to  run  for  thirty  minutes  before  breaking  circuit, 
and  note  the  time  again. 

(6)  Remove  the  coils  from  the  solution;  dry  them  carefully  by 
rolling  them  on  pieces  of  white  filter  paper,  then  by  dipping  into 
strong  alcohol  and  again  rolling  on  filter  paper.  The  alcohol  will 
quickly  evaporate,  leaving  the  coils  dry. 

(c)  Weigh  all  four  coils  again,  and  compare  their  weights  with 
those  previously  obtained.  It  will  be  found  that  the  small  coils  have 
gained  in  weight,  and  that  the  large  ones  have  lost  by  almost  the 
same  amount.  If  the  experiment  has  been  carefully  carried  out,  it 
will  be  found  that  the  gaining  coils  increase  by  almost  precisely  the 
same  amount.  The  change  in  the  weight  of  the  losing  coils  is  less 
to  be  depended  upon.  To  compute  the  average  strength  of  current 
which  has  passed  through  the  voltameter  during  the  experiment,  we 
divide  the  increase  of  weight  of  each  in  grams  by  the  number  of 
seconds  of  time  during  which  the  current  has  been  flowing.  This,  in 
turn,  is  divided  by  the  quantity  0-000328,  which  is  the  amount  of 
copper  in  grams  deposited  by  one  ampere  of  current  in  a  second 
of  time.  The  result  gives  the  average  strength  of  the  current  in 
amperes.  By  means  of  a  balance  of  proper  delicacy  current  may  be 
measured  in  this  to  within  a  fraction  of  one  per  cent. 

281.  The  Silver  Voltameter.  —  In  this  apparatus  a  silver 
anode  is  used,  and  a  kathode  consisting  of  a  platinum 
bowl,  which  serves  at  the  same  time  as  the  containing 
vessel  for  the  solution.  The  solution  consists  of  silver 
nitrate  dissolved  in  water.  By  the  electrolytic  action  the 
nitrate  of  silver  in  the  solution  is  decomposed,  and  the 


314 


THE  OUTLINES   OF  PHYSICS 


silver  is  deposited  in  the  form  of  minute  crystals  upon 
the  surface  of  the  platinum  dish.  The  free  nitric  acid 
which  is  produced  at  the  anode  attacks  the  latter  and  eats 
it  away.  This  instrument  is  capable  of  as  high  a  degree 
of  accuracy  as  the  copper  voltameter,  but  it  is  less  con- 
venient for  laboratory  purposes  on  account  of  the  costly 
materials  used  and  of  the  corrosive  nature  of  the  solution 
employed  as  an  electrolyte. 

282.  Electrochemical  Equivalents.  —  If  voltameters  em- 
ploying various  substances  are  placed  in  the  same  circuit, 
so  that  the  same  current  passes  through  them  all,  the 
products  of  the  electrolytic  action  will  be  found  to  differ, 
according  to  the  metals  deposited,  in  a  perfectly  definite 
manner.  The  amount  of  each  metal  deposited  is  propor- 
tional to  its  atomic  weight,  and  is  found  by  dividing  that 
quantity  by  its  valency.  The  amount  of  any  metal  which 
will  be  deposited  by  an  ampere  of  current  in  a  second  of 
time  is  called  its  electrochemical  equivalent.  The  elec- 
trochemical equivalent  of  a  few  of  the  substances  most 
frequently  employed  in  electrolysis  are  given  in  the  fol- 
lowing table : 

TABLE  OP  ELECTROCHEMICAL  EQUIVALENTS. 


Element. 

Electrochemical 
equivalent  (grams  per 
ampere  per  second). 

Element. 

Electrochemical 
equivalent  (grams  per 
ampere  per  second). 

Hydrogen  .     .     . 

0-00001038 

Oxygen    .     . 

0-000082 

Copper  .... 

0-000328 

Chlorine  .     . 

0-000367 

Gold      .... 

0-000679 

Iodine  .     .     . 

0-001314 

Lead     .... 

0-001072 

Bromine  .     . 

0-000828 

Nickel  .... 

0-000304 

Silver    .... 

0-001118 

Zinc.     .     .     .     . 

0-000337 

THERMO-ELECTRICITY 


315 


CHAPTER   XXXII 
THERMO-ELECTRICITY 

283.  The   Production  of   Current   by   Means   of   Heat  — 
Whenever  in  an  electric  circuit  we  have  two  metals,  and 
a   difference   of   temperature   exists    between   the   places 
where  these  metals  are  joined,  current  will  flow  through 
the  circuit.     If,  in  Fig.  278,  A  and  B  are  the  junctions 
between  iron  and  copper,  and  if  A  be  heated  by  means  of 
a   flame,   the    current   will 

flow  in  the  direction  indi- 
cated by  the  arrow.  If  B 
be  heated  instead  of  A,  the 
flow  will  still  be  from  copper 
to  iron,  but  in  the  opposite 
direction.  Currents  gener- 
ated in  this  way  are  called  thermo-electric  currents,  and 
the  arrangement  of  two  metals  is  called  a  ther  mo-element. 

284.  The  Thermopile.  —  The  difference  of  potential  pro- 
duced by  heating  one  junction  of  the  thermo-element  de- 
pends upon  the  metals  which  are 

employed.  The  greatest  effect 
attainable  with  ordinary  materials 
occurs  when  bismuth  and  antimony 
form  the  two  metals  of  the  ele- 
ment. The  difference  of  potential 
may  be  further  augmented  by  placing  a  large  number  of 
such  thermo-elements  in  series,  as  shown  in  Fig.  279;  a  bar 


316  THE  OUTLINES   OF  PHYSICS 

of  antimony  soldered  to  a  bar  of  bismuth,  and  this  to  the 
second  bar  of  antimony,  and  so  on  indefinitely. 

If  we  heat  the  alternate  junctions  a,  c,  e,  #,  etc.,  of  such 
an  arrangement,  the  difference  of  potential  at  the  ends  of 
the  series  is  the  sum  of  those  produced  in  each  element. 
Such  a  combination  of  thermo-elements  is  called  a  thermo- 
pile. In  order  to  give  it  as  compact  a  form  as  possible, 
the  thermopile  is  made  of  parallel  bars  of 
antimony  and  bismuth,  with  an  insulating 
layer  of  mica  between  each.  These  are  usu- 
ally arranged  in  the  form  of  a  cubical  block, 
mounted  as  shown  in  Fig.  280.  The  bars 
are  connected  together  in  such  a  manner 
that  alternate  junctions  lie  together  upon 
one  face  of  the  block.  When  used  with  a 
FIG.  280.  suitably  sensitive  galvanometer,  very  small 
differences  of  temperature  between  the  faces  of  the  ther- 
mopile may  be  measured. 

285.  The  Peltier  Effect.  —  In  1834,  the  physicist  Peltier 
discovered  that  when  the  electric  current  is  sent  through 
a  circuit  containing  a  thermo-element,  one  junction  will  be 
heated  and  the  other  cooled ;  also,  that  the  distribution  of 
temperatures  is  such  as  would  tend  to  form  a  thermo- 
electric current  flowing  in  the  opposite  direction  from  that 
which  produces  this  difference  of  temperature.     This  phe- 
nomenon is  called  the  Peltier  effect.     It  may  be  illustrated 
by  means  of  the  following  experiment : 

286.  EXPERIMENT  90. —  The  Peltier  Effect  in  a  Thermopile. 
Apparatus  : 

(1)  A  thermopile  and  galvanometer. 

(2)  A  bichromate  battery  consisting  of  three  or  four  cells. 


THERMO-ELECTRICITY 


317 


Procedure : 

(a)  Connect  the  thermopile  with  the  terminals  of  the  galvanometer. 
Touch  one  face  of  the  pile  for  an  instant  with  the  finger,  thus  warm- 
ing it  slightly,  and  notice  the  direction  in  which  the  galvanometer 
needle  is  deflected. 

(6)  Disconnect  the  galvanometer  and  the  thermopile.  Connect  the 
latter  with  the  battery  for  a  few  seconds,  then  disconnect  and  reattach 
to  the  galvanometer.  There  will  be  a  deflection  produced  this  time  by 
the  relative  heating  and  cooling  of  the  faces  of  the  thermopile  by  the 
passage  of  the  current,  and  this  will  die  away  as  the  temperature  dis- 
tributes itself  within  the  pile.  The  direction  of  this  deflection  will 
depend  upon  the  way  in  which  the  battery  was  connected  with  the 
thermopile. 

(c)  Repeat  operation  (6),  reversing  the  connections  between  the 
thermopile  and  the  battery.  Note  that  the  galvanometer  deflection  is 
reversed.  It  appears  from  this  experiment  that  a  sufficient  difference  of 
temperature  may  be  produced  by  sending  the  electric  current  through 
a  thermopile  to  give  thermo-electric  currents,  and  that  the  direction 
of  these,  and  consequently  the  nature  of  the  heating  and  cooling  of 
the  junctions,  depends  upon  the  direction  of  the  current  which  pro- 
duced them.  It  is  easier  to  establish  the  remaining  fact  of  importance 
with  reference  to  the  Peltier  effect ;  namely,  that  the  thermo-electric 
current  flows  in  a  direction  such  as  to  oppose  the  current  which  pro- 
duces it,  by  means  of  an  apparatus  to  be  described  in  the  following 
experiment : 

287.  EXPERIMENT  91.  — Direction  of  the  Thermo-electric  Current 
in  an  Element  of  Antimony  and  Bismuth. 

Apparatus : 

(1)  A  bar  of  bismuth  about  10  cm.  long  and  1  cm.  in  diameter 
soldered  at  the  ends  to  similar  bars  of  antimony.  These  at  their  free 


FIG.  281. 

ends  are  also  soldered  to  copper  wires,  and  the  whole  is  mounted  upon 
a  wooden  block,  as  shown  in  Fig.  281. 


318  THE  OUTLINES   OF  PHYSICS 

The  bars  of  antimony  and  bismuth  necessary  for  the  construction 
of  this  apparatus  may  be  obtained  by  pouring  the  molten  metals  into 
small  test  tubes ;  after  the  metal  has  been  solidified,  the  tubes  may  be 
broken  and  the  bars  thus  obtained  may  be  dressed  with  a  file  and 
soldered  together.  Great  care  must  be  taken  in  handling  bismuth,  on 
account  of  the  brittle  nature  of  this  semicrystalline  metal. 

(2)  The  galvanometer  used  in  the  foregoing  experiment. 

(3)  A  bichromate  battery. 

(4)  A  resistance  box ;  one  containing  several  thousand  ohms  is  to 
be  preferred. 

Procedure  : 

(a)  Connect  the  zinc  pole  of  one  cell  through  the  resistance  box 
with  one  terminal  of  the  galvanometer.  Take  the  wire  running  from 
the  carbon  pole  in  the  right  hand  and  make  momentary  contact 
with  the  other  terminal  of  the  galvanometer.  Note  the  direction  in 
which  the  needle  is  deflected. 

(6)  Connect  the  galvanometer  with  the  antimony-bismuth  thermo- 
element above  described,  as  shown  in  Fig.  282.  Warm  slightly  first 
one  and  then  the  other  of  the  junctions 

DIRECTION  OF  CURRENT  i       ,  u  •  j_l  i  j.'  i 

between  bismuth  and  antimony,  and  note 
the  deflections  of  the  galvanometer.  Hav- 
ing determined  which  one  must  be  heated 
in  order  to  send  the  current  through  the 
galvanometer  in  the  same  direction  as 
when  the  cell  was  employed,  trace  out 
the  direction  of  current  in  the  thermo- 
element. It  will  be  found  that  when  a 
junction  between  antimony  and  bismuth  is  heated,  the  current  always 
flows  from  bismuth  to  antimony  through  the  heated  junction. 

(c)  Test  the  direction  of  the  Peltier  effect  as  follows :  Disconnect 
the  galvanometer  and  connect  the  thermo-element  with  three  or  four 
cells  of  the  bichromate  battery,  for  about  thirty  seconds,  noting  the 
direction  in  which  the  current  flows  through  the  element.  Disconnect 
and  make  connection  with  the  galvanometer  again,  taking  care  to 
arrange  the  circuit  precisely  as  in  operation  (&).  Note  the  direction 
of  the  deflection.  It  will  be  found  that  the  deflection  indicates  the 
production  of  a  difference  of  temperature  such  as  to  create  a  thermo- 
electric current  flowing  in  the  opposite  direction  through  the  element 
from  the  current  which  produced  it. 


THERMO- ELECTE1CITY  319 

288.  The    Thermo-electric    Series.  —  By   testing   various 
metals  in  pairs  at  a  given  temperature,  and  determining 
the  size  and  direction  of  the  thermo-electric  currents  pro- 
duced when  a  difference  of  one  degree  of  temperature  is 
created  between  the  junctions,  it  is  possible  to  arrange  the 
various  metals  tested  in  a  series,  such  that  the  current  in 
the  heated  junction  will  flow  from  any  metal  through  the 
junction   into  metals  lower  down  in  the  series,  and  vice 
versa.     The  following  is  such  a  series,  in  which  lead  is 
selected  as  the  neutral  metal  with  which  all  others  are  to 
be  compared.     It  is  made  out  for  the  temperature  interval 
19°-20°  C. 

THERMO-ELECTRIC  SERIES. 

+  Silver. 

Bismuth.  Zinc. 

German  silver.  Copper. 

Lead.  Iron. 

Platinum.  Antimony. 
Gold. 

289.  The  Neutral  Point.  —  Such  a  series  as  the  above  is 
applicable  only  to  the  temperature  in  question.    It  is  found, 
in  fact,  that  for  any  given  pair  of  metals  the  thermo-elec- 
tric effect  varies  with  the  temperature  at  which  the  ex- 
periment is  performed.     Frequently  the  effect  disappears 
altogether  when  a  certain  temperature  is  reached,  and  then 
becomes  reversed.    The  point  at  which  this  reversal  occurs 
is  called  the  neutral  point  for  those  metals.    This  fact  may 
be  illustrated  by  means  of  the  following  experiment : 

290.  EXPERIMENT  92.— The  Neutral  Point  for  Iron  and  Copper. 

Apparatus : 

(1)  A  piece  of  iron  wire  about  1  m.  long;  copper  wire  and  a  gal- 
vanometer. 

(2)  A  Bunsen  burner. 


320 


THE  OUTLINES   OF  PHYSICS 


Procedure: 

(a)  Form  junctions  between  the  iron  and  copper  wires  by  twisting 
together  the  ends,  which   should    have    been   previously  cleaned   by 
scraping.     In  this  way  the  use  of  solder  is  avoided.     Connect  the  free 
ends  of  the  copper  wire  to  the  terminals  of  the  galvanometer. 

(b)  Carefully  heat  one  junction  with  the  Bunsen  burner  and  watch 
the  effect  upon  the  galvanometer.     It  will  be  seen  that  as  the  temper- 
ature of  this  junction  rises, 
the  deflection  increases  to 
a  certain  value   and  then 
diminishes    again,  passing 
through  the  zero  point  and 
changing   sign.     There   is, 
in  fact,  a  neutral  point  be- 
tween copper   and   iron  at 
about  275°  C.     If  we  were 
to  measure  temperature  dif- 
ferences of  the  junctions, 
as  well  as   deflections,  we 

should  be  able  to  plot  a  curve  like  that  in  Fig.  283.  Such  peculiarities 
in  the  behavior  of  the  thermo-elements  make  it  necessary  to  study  the 
thermo-electric  effect  very  carefully  before  using  it  for  the  measure- 
ment of  temperatures. 


ELECTROMAGNETIC  INDUCTION  321 


CHAPTER   XXXIII 

ELECTROMAGNETIC  INDUCTION 

291.  The  Production  of  a  Current  in  a  Wire  by  Cutting 
Lines  of  Force.  —  If  a  wire  be  moved  in  a  magnetic  field 
in  such  a  direction  as  to  cut  the  lines  of  force,  an  electric 
current  will  be  set  up  in  the  wire.     A  current  thus  pro- 
duced is  called  an  induced  current.     Its  source  is  the  work 
required  to  move  the  wire  through  the  magnetic  field. 
The  existence  of  such  currents  may  be  demonstrated  by 
means  of  the  following  experiment : 

292.  EXPERIMENT  93.  —  The  Study  of  Currents  induced  by  mov- 
ing a  Wire  in  the  Magnetic  Field. 

Apparatus : 

(1)  The  galvanometer  previously  described ;  a  piece  of  wire  several 
meters  in  length. 

(2)  An  electromagnet  and  battery. 
Procedure : 

(a)  Connect  the  ends  of  the  wire  to  the  terminals  of  the  galva- 
nometer, forming  a  closed  circuit.  At  a  distance  of  at  least  3  or  4  m. 
from  the  galvanometer,  set  up  the  electromagnet,  connecting  it  with 
the  poles  of  the  bichromate  battery ;  the  latter  should  consist  of  at 
least  4  to  6  cells. 

(6)  Close  the  battery  circuit,  and  allow  the  galvanometer  needle 
to  come  to  rest.  Take  the  wire  connected  with  the  galvanometer, 
holding  a  piece  of  the  same  near  the  middle,  stretched  between 
both  hands.  Move  this  wire  downward  and  through  the  field  of 
the  electromagnet  from  above,  so  as  to  cut  the  lines  at  right  angles, 
as  shown  in  Fig.  284.  Observe  the  effect  upon  the  galvanometer 
needle.  Repeat  this  movement,  but  in  a  reverse  direction,  and  note 
that  the  deflection  is  reversed.  Move  the  wire  at  uniform  speed 

Y 


322  THE  OUTLINES   OF  PHYSICS 

through  weak,  and  then  through  very  strong,  parts  of  the  field,  and 
notice  that  in  the  strong  field,  where  the  lines  of  force  are  most  plen- 
tiful, the  effect  is  greatest.  Move  the 
wire  down  from  outside  the  field  to  a 
position  midway  between  the  polepiece 
of  the  magnet,  and  bring  it  to  rest 

!i there.     Note   that,  as.  the   motion    of 

the  wire   ceases,  the   induced   current 
N  ceases  to  flow,  although   the  wire   re- 

mains in  a  very  strong  part  of  the 
field.  Move  the  wire  as  nearly  as  pos- 
sible in  the  direction  of  the  lines  of 
force,  instead  of  across  them,  and  note 
that  the  induced  current  can  thus  be 
FlG  98i  diminished  almost  to  zero.  Were  it 

possible   to   move  the  wires   so   as   to 
cut  no  lines  of  force,  no  induced  current  would  show  itself, 
(c)  The  direction  of  the  induced  current  is  determined  thus  : 
Lines  of  force  which  have  a  common  direction  repel  each  other. 
When  we  move  a  wire  in  the  magnetic  field,  lines  of  force  are  set  up 

in  such  a  direction  as  to  resist  its  mo- 
^    tion.    The  lines  of  force  created  around 

\?^ 

0<c  the  wire  are  circles,  and  the  positive 

^N°  direction  around  these  circles  is  clock- 

wise to  the  person  looking  along  the 
wire  in  the  direction  in  which  the  cur- 
rent is  flowing.  (See  Fig.  285.)  Bear- 

x^^ v  ing  this  convention  in  mind,  proceed 

FIG.  285.  to  verify  the  statement  that  fhe  direc- 

tion of  the  induced  current  is  such  as 

to  impede  the  motion  of  the  wire  through  the  field.  For  this  purpose, 
test  the  poles  of  the  electromagnet  by  means  of  a  compass  needle,  or 
with  the  floating  magnet  needle  used  in  previous  experiments. 

The  lines  of  force  between  the  pole  of  the  electromagnet  are 
to  be  considered  as  issuing  from  the  north  pole  and  entering  the 
south  pole.  If,  therefore,  the  experimenter  stands  facing  the 
magnet  with  the  north  pole  to  his  right  hand,  these  lines  will  run 
from  right  to  left ;  if  the  wire  be  moved  downward  through  this  field, 
the  current,  which  will  retard  its  motion,  is  one  such  that  the  circular 


ELECTE OMA  GNETIC  IND  UCTION 


323 


lines  around  the  wire  are  parallel  to  the  lines  of  the  field  beneath  the 
wire.  This  means  that  they  are  clockwise  to  the  observer,  and  that 
the  current  is  flowing  through  the  wire  in  the  direction  in  which  he 
looks.  Having  moved  the  wire  down  in  the  manner  just  described, 
and  noted  the  direction  of  the  galvanometer  deflection,  test  this  point 
by  opening  the  galvanometer  circuit,  and  introducing,  for  an  instant, 
a  single  voltaic  cell.  Connect  this  cell  so  that  the  deflection  will  be 
as  above ;  then  trace  out  the  direction  of  the  current. 


293.  The  fact  that  a  conductor,  moving  in  the  magnetic 
field,  meets  with  resistance  to  its  motion,  may  be  demon- 
strated in  numerous  ways.  One  of 
the  simplest  experiments  for  this  pur- 
pose consists  in  mounting  a  pendulum 
of  the  form  shown  in  Fig.  286  be- 
tween the  poles  of  an  electromagnet. 
So  long  as  the  magnet  is  inactive,  this 
copper  pendulum  swings  freely.  If, 
however,  the  current  be  sent  through 
the  coils  of  the  magnet,  thus  creating 
a  strong  field,  the  copper  pendulum 
will  experience  such  resistance  to  its 
passage  across  the  lines  of  force  that 
it  will  be  brought  to  rest  before  it 
completes  a  single  vibration.  The 
experiment  is  a  striking  one  and  may  be  easily  tried ;  it  is 
instructive  to  attempt  to  move  the  sheet  of  copper  sud- 
denly in  the  field  by  means  of  the  hand.  The  resistance 
which  manifests  itself  may  then  be  directly 
felt. 

If  a  second  copper  disk  similar  to  the 
first,  but  cut  nearly   through    with   the 
shears  in  a  series  of  vertical  slits,  as  shown  in  Fig.  287, 
be  substituted  for  the  pendulum  above  described,  it  will 


FIG.  286. 


FIG.  287. 


324  THE  OUTLINES   OF  PHYSICS 

be  found  that  it  experiences  comparatively  little  opposi- 
tion when  swinging  in  the  magnetic  field.  The  reason  is 
that  the  vertical  slits  in  the  copper  interfere  with  the  cir- 
culation of  the  induced  currents.  These  being  less  power- 
ful, comparatively  few  lines  of  force  are  formed  round  the 
moving  mass.  Such  a  pendulum  will  make  several  vibra- 
tions in  the  field  of  the  electromagnet  before  coming 
to  rest. 

294.  Force  exerted  upon  a  Wire  carrying  Current  in  the 
Magnetic  Field.  —  The  phenomenon  described  in  the  first 

^    article  of  this  chapter  is 
O<GO**       a  reversible  one.     Any 


X^~  netic    field    in   such   a 

position  that  it  is  not 

>•  FIELD 

^  parallel    to    the    lines 

of     force,    and    which 

has   a  current   flowing 
DOWNWARD  through     it,    is    acted 

FORCE  ACTING 

upon  by  a  force  which 
tends    to    move    it   at 

FlG  988.  right  angles  to  its  own 

length,  and  to  the  direc- 
tion of  the  lines  themselves.     (See  Fig.  288.) 

This  force  may  be  conveniently  considered  to  be  that 
with  which  the  lines  of  force  of  the  magnetic  field,  and  those 

m — vm  due  to  the  current  within  the  wire,  repel 

cf~\c  eacn  other  upon  that  side  of  the  wire 

where  they  are  parallel,  and  in  the  same 

!/  direction.     Let  mm  and  cc  (Fig.  289)  be 

I  portions  of  lines  of  force  due  to  the  mag- 

FIG.  289.  net  and  to  the  current  within  the  wire. 


ELECTROMAGNETIC  INDUCTION 


325 


These  repel  each  other,  and  the  direction  of  the  force, 
which  may  be  considered  as  acting  upon  the  wire,  will  be 
that  of  the  arrow  /  shown  in  the  figure.  By  means  of 
the  conception  of  lines  of  force  and  their  mutual  action, 
we  can  always  ascertain  what  the  forces  acting  upon  a 
current  in  the  field  will  be,  and  even  their  size  and  direc- 
tion. The  existence  of  the  forces  acting  upon  electric  cir- 
cuits in  the  magnetic  field  may  be  shown  in  a  great  variety 
of  ways.  One  of  the  simplest  devices  is  described  below  : 

295.   EXPERIMENT  94.  —  Attractive  and  Repellent  Forces  between 
a  Magnet  and  a  Wire  carrying  Current;    also  between  Two  Circuits. 

Apparatus : 

(1)  The  arrangement  shown  in  Fig.  290.      This  consists  of  two 
parallel  wires,  each  bent  into  the  rectangular  form  shown  in  the 
figure. 

These  are  hung  side  by  side  about  2  cm.  apart  from  a  wooden 
block  by  means  of  strips  of  thin  copper  foil. 

(2)  The  bichromate  battery. 

(3)  A  horseshoe  magnet. 


FIG.  290. 


FIG.  291. 


326  THE  OUTLINES  OF  PHYSICS 

Procedure : 

(a)  Send  current  from  the  battery  through  one  of  the  wires. 
Hold  the  magnet  near,  as  shown  in  Fig.  291,  and  note  the  attraction 
or  repulsion  of  the  wire  according  to  the  position  of  the  magnet 
poles.  Trace  out  the  course  of  the  current,  and  the  relations  of  its 
lines  of  force  to  those  of  the  field  of  the  magnet.  Show  that  the 
behavior  of  the  wire  follows  the  principle  laid  down  in  Art.  294. 

(&)  Send  current  through  both  wires,  and  note  that  the  wires 
attract  each  other  when  the  currents  flow  in  the  same  direction,  and 
repel  each  other  (Fig.  292)  when  they  flow  in  opposite  directions.* 

The  French  physicist,  Ampere,  has  stated  this  mutual  action  of 
electric  currents  as  follows  : 

(1)  Parallel  conductors  carrying  current  in  the  same  direction  attract 
each  other.  (2)  Parallel  conductors  carrying  current  in  opposite  direc- 
tions repel  each  other. 


©  © 

ATTRACTION 

©    © 


REPULSION 

FIG.  292.  FIG.  293. 

The  effect,  from  the  point  of  view  of  the  mutual  action  of  lines 
of  force,  is  indicated  in  Fig.  310.  Ampere  pointed  out  likewise  that 
two  conductors  carrying  current  which  make  an  angle  with  one 
another  will,  if  free  to  move,  arrange  themselves  parallel  to  one 
another,  and  with  the  current  flowing  through  them  in  the  same 
direction. 

296.  Dynamos  and  Motors.  —  Upon  the  principles  devel- 
oped in  the  foregoing  experiments  of  this  chapter,  two 
very  important  forms  of  electrical  apparatus  are  con- 
structed ;  these  are  the  dynamo  and  the  motor.  The 
former  is  a  machine  for  the  production  of  electric  currents 


ELECTROMAGNETIC  INDUCTION  327 

by  the  motion  of  conductors  across  the  lines  of  force  in 
the  magnetic  field.  The  latter  is  a  machine  for  the 
development  of  power  by  the  movement  of  conductors 
under  the  action  of  the  magnetic  field. 


FIG.  294. 


To  obtain  the  principle  of  the  dynamo  in  its  simplest 
form  consider  a  loop  of  wire  which  moves  in  the  field  as 
shown  in  Fig.  294.  This  is  free  to  revolve  upon  ab  as 
an  axis,  between  the  poles  of  an  electromagnet.  If  the 
wire  be  made  to  revolve  in  the  direction  of  the  arrow, 
it  will  cut  the  lines  of  force  of  the  field  at  first  very 
slowly,  and  then  more  and  more  rapidly.  When  it  has 
reached  the  position  shown  in  the  dotted  line,  where 
its  motion  is  perpendicular  to  the  lines  of  force,  it  cuts 
them  at  the  highest  rate.  After  passing  this  posi- 
tion, it  cuts  fewer  and  fewer  lines,  until  it  reaches  the 
position  180°  away  from  its  starting  point,  where  it 
again  moves  parallel  to  the  lines  and  cuts  none.  The 
result  of  this  motion  is  a  surge  of  current  through  the 
wire,  which  rises  to  a  maximum  and  dies  away  again. 
During  the  remainder  of  its  revolution  the  wire  will  cut 
lines  of  force  again;  at  first  at  an  increasing  rate,  then 
more  and  more  slowly.  But  these  will  be  cut  in  such  a 
way  as  to  send  the  current  in  the  opposite  direction. 
Such  a  revolving  wire,  with  arrangements  for  carrying 
currents  into  an  outer  circuit,  would  be  an  alternating 
current  dynamo  of  the  simplest  type.  To  change  this 
alternating  current  into  a  direct  current,  that  is  to  say, 


328 


THE  OUTLINES   OF  PHYSICS 


into  a  current  which  is  always  flowing  in  the  same  direc- 
tion, a  device  called  a  commutator  is  employed.  This 
consists  of  two  sliding  contacts  of  metal  or  of  carbon, 
called  brushes,  which  rest  upon  a  divided  collar  attached 
to  the  axle  (Figs.  295  and  296).  By  this  means  one 


FIG.  295. 


FIG.  296. 


terminal  of  the  outer  circuit  is  connected  half  the  time 
with  one  end  of  the  loop  of  wire,  the  other  half  of  the 
time  with  the  other,  so  that  the  current  always  flows 
through  the  outer  circuit  in  the  same  direction.  In 
actual  dynamo  machines  there  is  a  great  number  of  these 
loops  of  wire,  which  follow  one  another  through  the  field 
continually.  They  are  so  connected  together  and  to  the 
commutator  that  each  furnishes  its  share  of  current  to 
the  outer  circuit  in  succession.  This  revolving  combi- 
nation of  loops  or  coils  is  called  the  armature  of  the 
dynamo.  There  is  no  space  in  the  present  work  to 
describe  the  many  types  of  machines  which  are  based 
upon  the  above-mentioned  principles. 

The  electric  motor  is  in  principle  of  construction  pre- 
cisely similar  to  the  dynamo.  The  distinction  is  that  in 
this  machine  current  from  some  outside  source  is  sent 
through  the  wires  of  the  armature.  These  then  are  acted 
upon  by  the  lines  of  force  of  the  field  as  described  in 
Art.  294.  The  machine  is  so  arranged  that  all  the 


ELECTROMAGNETIC  INDUCTION  329 

forces  acting  upon  the  different  wires  in  the  armature 
work  together.  The  armature  is  thus  given  a  rapid 
motion  of  rotation,  and  is  capable  of  doing  work. 

297.    EXPERIMENT  95.  —  The  Production  of  Induced   Currents  by 
the  Starting  or  Stopping  of  Currents  in  a  Neighboring  Circuit. 

Apparatus : 

(1)  The  coil  of  wire  wound  upon  an  Argand  chimney,  previously 
described. 

(2)  A  coil  of  smaller  diameter  and  of  about  the  same  length,  wound 
uppn  a  glass  tube  of  about  2  cm.  in  diameter. 

(3)  A  bundle  of  iron  wire. 

(4)  The  galvanometer  previously  described. 

(5)  The  bichromate  battery. 
Procedure  : 

(a)  Connect  the  terminals  of  the  galvanometer  with  those  of  the 
larger  coil,  and  the  ends  of  the  smaller  coil  with  the  terminals  of  the 
battery,  leaving  the  latter  cir- 
cuit open.     (See  Fig.  297.) 

(b)  Close  the  battery  circuit 
suddenly  and  notice  the  effect 
upon  the  galvanometer  needle. 
It  will  be  seen  that  the  latter  is 
suddenly  deflected,  but  not  per- 
manently so,  and  that  it  comes 
to  rest  in  its  old  position.   Break 
the   battery  circuit   again,  and 
note  that  an  equal  and  opposite 

deflection  of   the  galvanometer  needle  is  produced. 

(c)  Determine  by  the  use  of  a  single  cell  of  battery  the  direction 
of  current  in  the  outer  coil  indicated  by  these  two  deflections,  and 
compare  this  ^ji-ection  with  that  of  the  current  due  to  the  battery 
within  the  inner  coil.    It  will  be  found  that  the  direction  of  the  induced 
current  when  the  circuit  is  closed  is  opposite  to  that  of  the  inducing  current ; 
and  that  when  the  circuit  is  broken  the  induced  current  has  the  same  direc- 
tion as  that  which  has  been  destroyed.    The  creation  of  a  current  flowing 
in  the  inner  coil  is  similar  in  its  effect  to  the  very  rapid  movements 
of  a  magnet,  the  lines  of  force  of  which  correspond  to  those  of  this 


330 


THE  OUTLINES   OF  PHYSICS 


current,  from  an  infinite  distance  to  its  position  within  the  coil.  The 
opening  of  circuit  may  be  similarly  compared  to  the  sudden  with- 
drawal of  this  magnet  to  a  great  distance. 

(rf)  To  show  that  this  form  of  electromagnetic  induction  depends 
upon  the  action 'of  lines  of  force,  and  increases  with  the  number  of 
these,  the  bundle  of  wires  may  be  introduced  into  the  inner  coil. 
These  act,  on  account  of  their  high  permeability,  to  enable  the  pro- 
duction of  a  greatly  increased  number  of  lines  of  force. 

When  the  circuit  is  closed,  all  of  these  lines  of  force  may  be  con- 
sidered as  having  been  made  to  cut  the  wires  of  the  outer  coil.  The 
result  is  a  greatly  increased  deflection.  When  the  circuit  is  open 
again  it  is  as  though  these  numerous  lines  of  force  were  drawn  in 
again ;  cutting  the  coils  in  the  opposite  direction,  and  likewise  pro- 
ducing a  large  deflection. 

298.  Induction  Coils.  —  The  foregoing  experiment  indi- 
cates the  principle  upon  which  the  interesting  piece  of 
apparatus  called  the  induction  coil  is  constructed.  This 
consists  of  an  iron  core  a  (Fig.  298)  surrounded  by  a  coil 


FIG.  298. 


FIG.  299. 


of  wire  b  consisting  generally  of  a  few  turj^^toire.  This 
is  called  the  primary  coil.  It  in  turn  i^suwiunded  by 
a  large  coil  c  consisting  of  very  many  turns  of  very  fine 
wire.  The  ends  of  the  latter,  which  is  called  the  second- 
ary coil,  are  attached  to  a  pair  of  terminals  similar  to  those 
used  upon  the  Holtz  machine.  In  order  to  break  the  cir- 


ELECTROMAGNETIC  INDUCTION  331 

cuit  through  the  primary  coil,  a  device  called  an  inter- 
rupter is  employed.  This  is  frequently  given  the  form 
shown  in  Fig.  299.  It  consists  of  a  metal  spring,  to  one 
end  of  which  is  attached  a  disk  of  iron.  The  spring  is 
mounted  in  such  a  position  that  the  disk  is  opposite  the 
end  of  the  iron  core  of  the  coil.  The  current  from  the 
battery  flows  through  this  spring,  and  it  makes  its  exit  by 
the  way  of  a  metal  screw  which  touches  the  spring  at  the 
point  C.  Thence  the  current  passes  through  the  primary 
coil  back  to  the  battery.  The  current  through  the  coil 
magnetizes  the  core,  and  the  disk  at  the  end  of  the  spring 
is  attracted.  Its  movement  toward  the  core  draws  the 
spring  away  from  the  screw  at  C  and  breaks  the  circuit  at 
that  point.  The  current  then  ceases  to  flow  through  the 
primary  coil,  and  the  core,  which  is  of  soft  iron,  loses  its 
magnetism.  The  spring  of  the  interrupter  being  no  longer 
attracted  flies  back  to  its  original  position,  comes  into  con- 
tact with  the  screw  at  (7,  and  the  circuit  is  closed  again. 
This  process  goes  on  indefinitely  so  long  as  current  is 
allowed  to  flow,  inter- 
rupting the  current 
through  the  primary 
coil  many  times  a 
second. 

Each  time  the  cir- 
cuit closes,  a  magnetic 
field  is  formed  which 

embraces  both  the  pri- 

,     .  FIG.  300. 

mary  and  the  second- 
ary coils,  and  in  each  of  the  numerous  turns  of  the  second- 
ary coil  electromagnetic  induction  takes  place.     The  num- 
ber of  these  turns  is  very  large,  so  that  the  difference  of 
potential  between  the  terminals  is  enormous.     The  result 


332 


THE  OUTLINES   OF  PHYSICS 


is  that  a  spark  leaps  across  between  the  balls  of  the 
discharges  at  each  vibration  of  the  interrupter.  The 
sparks  thus  produced  are  similar  in  every  respect  to 
those  produced  by  influence  machines  or  by  any  electro- 
static device.  Induction  coils  have  been  constructed,  giv- 
ing sparks  as  much  as  a  meter  long.  Such  instruments 
have  secondary  coils  containing  hundreds  of  miles  of  fine 
wire.  Induction  coils  giving  a  spark  of  from  1  to  20  cm. 
are  very  common.  Figure  300  shows  the  usual  form  of 
induction  coil. 

299.   The   Telephone.  —  Another    important    instrument 
which  depends  for  its  action  upon  electromagnetic  induc- 
tion is  the  telephone.     This  in  its  simplest 
form  consists  of   a  permanent  bar  magnet 
(Fig.  301),  around  one  end  of  which  is  a 
coil  of  fine  wire.     Opposite  the  end  of  the 
bar    is    a    diaphragm    of    thin    sheet    iron 
against    which    the    sound   waves    of    the 
speaker's  voice  fall.     These  throw  the  dia- 
phragm into  vibration,  thus  causing  periodic 
fluctuations  in  the  magnetic  field  of  the  bar 
corresponding   to   the   pitch   of   the    voice. 
The  variations  in  the  field  induce  fluctuating 
currents  in  the  coil  of  wire. 
If  the  wires  are  connected  to  a  similar  instrument  at  a 
distant  station  (Fig.  302),  the  field  of  this  is  made  to  vary 
by  the  fluctuating  currents,  and  the  diaphragm  of  the  latter 


FIG.  301. 


RETURN  CIRCUIT  THROUGH  THE  EARTH 
FIG.  302. 


ELECTROMAGNETIC  INDUCTION  333 

instrument  vibrates  in  unison  with  that  of  the  former. 
Sound  waves  thus  produced  convey  speech  to  the  ear  of 
the  listener. 

These  telephonic  currents  are  exceedingly  weak.  In 
order  to  increase  them,  the  device  known  as  the  carbon 
transmitter  is  used.  This  consists  of  a  diaphragm,  a  stylus 
attached  to  the  middle  of  which  presses  against  a  mass 
of  powdered  carbon  compressed  into  a  disk  (Fig.  303). 
The  disk  forms  part  of  a  voltaic  circuit  as  shown  in  the 
figure.  The  vibrations 
of  the  disk  under  the  in- 
fluence of  sound  waves 
change  the  pressure  of 
the  stylus  upon  the  car- 


bon  and,  thereby,  the  re-  FlG  303 

sistance  of  the  latter. 

The  current  from  the  battery  B  which  flows  in  the 
circuit  fluctuates  in  response  to  these  vibrations.  It  flows 
through  the  primary  circuit  of  the  induction  coil  0  and 
induces  corresponding  currents  in  the  secondary  circuit. 
The  latter  is  connected  with  the  receiving  telephone  at 
the  distant  station,  the  diaphragm  of  which  thus  vibrates 
much  more  powerfully  than  if  it  were  of  an  ordinary  tele- 
phonic circuit. 


PAKT   IV— SOUND 


CHAPTER   XXXIV 
THE  PROPAGATION   OF   SOUND 

300.  Sound  Waves.  —  Sound  is  conveyed  to  the  ear  by 
means  of  a  wave  motion  of  the  air.     The  energy  of  sound 
waves  is  generally  small ;   although   in  the  case  of   the 
sounds  produced  by  explosions  —  by  the   firing   of   large 
guns,  etc. — decided  mechanical  effects  are  produced.    That 
there  is  a  mechanical  effect  produced  at  considerable  dis- 
tances, whenever  even  a  feeble  sound  is  made,  may  be 
shown  by  means  of  the  following  experiment: 

301.  EXPERIMENT  96.  — The  Sensitive  Flame. 
Apparatus: 

(1)  A  piece  of  rubber  tubing  such  as  is  used  to  convey  gas  to 
Bunsen  burners,  etc. 

(2)  Several  pieces  of  glass  tubing  of  such  size  as  to  fit  the  rubber 
tubing.     These  pieces  should  each  be  about  20  cm.  long. 

Procedure : 

(a)  Hold  each  of  these  glass  tubes  with  its  middle  in  the  Bunsen 
burner  until  the  glass  softens,  and  draw  it  out  until  the  diameter  in 


FIG.  304. 

the  contracted  portion  is  reduced  to  about  2  or  3  mm.  (See  Fig.  304.) 
After  having  thus  drawn  out  each  of  the  tubes,  cut  them  in  two  in  the 
middle  by  scratching  with  a  file  and  bending. 

334 


THE  PROPAGATION   OF  SOUND 


335 


(6)  Insert  the  large  end  of  one  of  the  tubes  thus  prepared  into  the 
free  end  of  the  rubber  hose  connected  with  the  gas  jet.  Turn  on  the 
gas  and  ignite  it  at  the  contracted  end  of  the  glass  tube.  If  the  pres- 
sure of  gas  is  sufficient  for  the  performance  of  this  experiment,  the 
flame  thus  produced  will  burn  with  a  slight 
roaring  noise,  and  show  a  perturbed  flame 
somewhat  similar  to  that  indicated  in 
Fig.  305  (a). 

1.  If  the  flame  in  question,  instead  of 
taking  this  form,  burns  quietly,  assuming 
the  form  shown  in  (&),  the  glass  tube  must 
be  discarded,  and  another  of  the  set  just 
made  must  be  tried.1  When  a  tube  has 
been  found  the  flame  from  which  roars 
in  the  manner  just  described,  turn  off  the 
gas  gradually  until  the  roaring  ceases. 
The  flame  will  then  change  over  into  the 
form  depicted  in  Fig.  305  b.  A  slight 
increase  in  the  supply  of  gas  will  restore 
it  to  the  perturbed  form.  There  is  an 
adjustment  between  these  two  conditions, 
such  that  the  flame  is  very  easily  changed 
from  the  quiet  to  the  roaring  form.  Such 
a  form  is  called  a  sensitive  flame.  When 
this  adjustment  has  been  made  it  will  be 
found  that  the  flame  changes  form  in  FlG-  305> 

response  to  nearly  every  sound  which  is  produced  in  the  room.  It  is 
especially  sensitive  to  shrill  or  sibilant  tones.  With  this  apparatus  one 
can  show  that  a  mechanical  disturbance  sufficient  to  transform  the  gas 
flame  from  the  quiet  to  the  roaring  state  into  which  it  tends  to  pass  is 
almost  instantaneously  produced  as  the  result  of  a  noise  in  the  most 
remote  corner  of  the  laboratory.  If,  for  example,  two  wooden  blocks 
be  struck  together  in  the  further  corner  of  the  room,  the  flame  re- 
sponds. The  jingling  of  a  bunch  of  keys  will  produce  the  same  result. 

1  In  some  localities,  especially  if  the  laboratory  is  situated  at  a  lower 
level  than  the  gas-works,  the  pressure  is  insufficient  to  produce  a  sensi- 
tive flame.  Under  such  circumstances  the  experiment  may  be  performed 
by  filling  an  ordinary  gas  holder  from  which  to  supply  the  flame.  The 
pressure  may  then  be  adjusted  at  will. 


336  THE  OUTLINES   OF  PHYSICS 

A  shrill  whistle  made  by  blowing  across  the  open  end  of  a  tube  is  also 
effective,  and  if  the  flame  be  properly  adjusted  the  utterance  of  any 
word  with  a  syllable  containing  a  sibilant  with  moderate  loudness,  or 
even  when  whispered,  will  suffice. 

Note  the  great  promptness  with  which  this  effect  follows  the  ex- 
citing cause.  A  moment's  consideration  will  show  that  no  air  draft 
could  traverse  the  intervening  space  with  sufficient  velocity  to  account 
for  this  promptness  of  response. 

2.  To  compare  the  time  required  for  a  draft  of  air  to  agitate  the 
•  flame,  with  that  needed  by  the  sound  wave,  turn  the  flame  down 
until  it  is  no  longer  sensitive,  then  step  back  for  a  distance  of  2  or 
3  m.,  face  the  flame  and  blow  towards  it  as  forcibly  as  possible.  Use 
a  short  tube  which  may  be  made  by  rolling  up  a  sheet  of  note  paper 
or  cardboard  to  direct  the  blast.  It  will  be  possible  in  this  way  to 
make  the  flame  flicker ;  but  the  interval  which  elapses  between  the 
puffing  sound  when  the-  air  passes  through  the  tube  until  the  flame 
shows  signs  of  agitation  is  very  appreciable,  whereas  the  response  of 
the  sensitive  flame  to  sound  waves  coming  from  several  times  the 
distance  in  question  is  too  prompt  to  admit  of  direct  observation. 

302.  Tyndall's  Experiment.  —  Professor  Tyndall  in  his 
lectures  on  sound  used  the  following  apparatus  for  showing 
that  it  is  a  true  wave  and  not  a  puff  of  air  which  effects 

the  sensitive  flame.     Tyn- 

^^==5=  a,   dall's  apparatus,  which  is 

n  *  depicted  in  Fig.  306,  con- 

sists of  a  long   tube  con- 
tracted to  a  nozzle  at  one 

end.  This  is  placed  in  a  horizontal  position,  and  a  lighted 
candle  is  mounted  with  the  flame  directly  in  front  of 
the  nozzle.  Upon  clapping  two  wooden  blocks  together 
at  the  other  end  of  the  long  tube,  the  candle  flame  responds 
by  a  sudden  movement.  To  show  that  this  is  the  result  of 
a  sound  wave  traveling  through  the  tube,  and  not  of  a 
draft  of  air  blown  out  from  between  the  blocks  and  travel- 
ing up  the  flame,  a  portion  of  the  air  within  the  tube  is 


THE  PEOPAGATION  OF  SOUND  337 

filled  with  smoke.  This  may  be  done  by  burning  within 
the  tube  a  bit  of  paper  previously  soaked  in  a  solution  of 
sodium  nitrate,  or  potassium  nitrate,  and  dried.  If  the 
smoky  air  thus  produced  be  observed  when  the  blocks  at 
the  open  end  of  the  tube  are  brought  together,  it  will  be 
possible  to  follow  its  movement.  It  will  be  seen  that 
while  it  is  agitated  for  an  instant  by  the  passage  of  the 
wave,  it  does  not  travel  through  the  tube  and  out,  but  is 
simply  disturbed  and  then  comes  to  rest  again.  There  is 
some  difficulty  in  performing  this  experiment,  owing  to 
the  fact  that  the  tube  is  apt  to  become  a  channel  for  feed- 
ing the  flame  with  air,  so  that  a  constant  draft  moving 
toward  the  nozzle  is  set  up  and  the  smoke  is  carried  along 
with  this  air  current.  There  is  little  danger,  however,  of 
confusing  this  slow  movement  of  the  smoke  toward  the 
flame  with  the  wave  which  causes  the  flame  to  jump  when 
the  blocks  are  clapped  together. 

A  sound  wave  in  air  consists  of  a  rapid  to  and  fro 
motion  (a  longitudinal  vibration)  of  the  particles  of  the 
gas,  in  the  direction  in  which  the  wave  travels.  If  we 
could  secure  a  picture  of  the  condition  of  the  air  in  a 
narrow  region  through  which  waves  were  moving,  we 
should  find  that,  instead  of  being  everywhere  equally 
dense,  there  are  successive  layers  of  great  density  (c?,  c?, 
Fig.  307),  with  intervening  layers  (r)  where  the  air  is 
rarefied.  The  vibration 
of  the  air  is  momenta- 
rily  in  the  directions  of 
the  small  arrows,  thus 
producing  condensation  T 
at  d,  d,  and  rarefaction 

at  r.  These  regions  of  condensation  and  rarefaction 
all  move  simultaneously  in  the  direction  of  the  large 


338 


THE  OUTLINES   OF  PHYSICS 


arrow,  without  changing  their  positions  relative  to  one 
another. 

303.  Sound  Waves  produced  by  a  Projectile.  —  Projectiles 
moving  at  high  speeds  produce  air  waves  which  are  similar 
^^^^^^^^^^^^^^^^^^^^^^  to  those  by  means 

of  which  sound  is 
transmitted  and 
which  travel  at  the 
same  velocity.  In- 
stantaneous photo- 
graphs of  such  pro- 
jectiles show  these. 
The  diagram  in  Fig. 
308  is  from  a  photo- 
graph of  a  rifle  bul- 
let in  flight,  taken 
by  Mr.  C.  V.  Boys 
in  England.  The 
oblique  lines,  a,  a, 
6,  6,  show  the 
positions  of  the 
waves. 


i 


FIG.  308. 

V 

304.  The  Velocity  of  Sound.  —  It  has  been  seen  in  the 
experiment  of  the  sensitive  flame  that  sound  waves  travel 
with  a  high  velocity.  It  is  only  necessary  to  recall  the 
following  observation,  which  every  one  will  have  had  fre- 
quent opportunity  to  make  for  himself,  to  show  that  this 
velocity  is  very  much  less  than  the  velocity  of  light.  If 
we  watch  a  distant  railway  train  when  the  whistle  is 
sounded  for  a  crossing  or  station,  we  may  notice  that  tho 
puff  of  steam  is  followed  only  after  a  very  considerable 


THE  PROPAGATION  OF  SOUND 


339 


interval,  depending  on  our  distance  from  the  engine,  by 
the  sound  of  the  whistle.  The  sight  of  the  puff  of  steam 
has  been  conveyed  to  the  eye  by  means  of  a  wave  of  light ; 
the  sound,  however,  which  occurs  simultaneously  with  the 
setting  free  of  the  steam,  by  a  sound  wave.  The  interval 
of  time  which  seems  to  elapse  between  the  two  is  therefore 
that  which  the  sound  wave  requires  to  traverse  the  space 
between  the  whistle  and  the  ear  of  the  observer,  over  that 
required  by  the  wave  of  light  to  traverse  the  same  distance. 
Light  waves  travel  at  such  very  great  velocity  (330,000,000 
m.  per  second),  that  we  may  neglect  the  time  occupied 
by  the  light  altogether.  By  stationing  one's  self  at  a 
measured  distance  from  the  point  at  which  the  railway 
train  whistles,  one  can  therefore  obtain  a  very  good  esti- 
mate of  the  velocity  of  sound.  This  velocity,  as  has  been 
determined  many  times,  is  about  332  m.  per  second  when 
the  air  is  at  0°  C.  With  rise  of  temperature  the  velocity 
rises.  At  20°  C.,  for  example,  it  is  about  343  m. 

305.    EXPERIMENT  97.  —  Sounds  will  not  travel  in  a  Vacuum. 

Apparatus : 

(1)  An  air  pump. 

(2)  A  receiver  with  an  open 
neck,  as  shown  in  Fig.  309. 

(3)  An  electric  bell. 

(4)  A    Leclanche     cell,    or 
other    battery   used    for  open 
circuits ;  also  a  key. 

Procedure  : 

(a)  Find  a  cork  which  will 
fit  the  neck  of  the  receiver. 
Bore  two  holes  through  the 
cork  and  insert  copper  wires, 

cementing  them  into  place.    To  

the  free  ends  of  these  wires,  a  FlG-  309> 

short  distance  within  the  receiver,  hang  the  electric  bell,  suspending 


340  THE  OUTLINES    OF  PHYSICS 

the  same  from  its  binding  posts  as  shown  in  the  figure.  Cover  the 
entire  outer  surface  of  the  cork  with  beeswax  and  rosin  cement,  so 
as  to  preclude  leakage. 

(b)  Attach  the  battery,  with  the  key  inserted,  to  the  outer  ends  of 
the  two  wires  which  have  been  used  in  the  suspension  of  the  bell. 
Place  the  bell  jar  upon  the  plate  of  the  air  pump.     Close  the  key  and 
note  the  sound  of  the  bell,  which  will  be  distinctly  heard,  although 
somewhat  muffled  by  being  inclosed  within  the  heavy  bell  jar. 

(c)  Exhaust  the  air  from  the  receiver  and  note  the  dying  away  of 
the  sound  of  the  bell. 

If  the  air  pump  be  in  good  condition,  and  the  sealing  of  the  neck 
of  the  receiver  be  really  tight,  the  exhaustion  can  be  carried  to  such 
a  point  that  it  is  very  difficult  to  detect  the  faintest  sound  from  the 
bell.  A  certain  small  amount  of  sound  will  always  find  its  way  out 
through  the  body  of  the  conducting  wires.  These  are  solids,  and  are 
capable  of  transmitting  sound  waves.  Upon  restoring  the  air  to  the 
receiver,  the  sound  of  the  bell  will  return  to  its  initial  loudness. 
From  such  experiments  as  this  we  conclude  that  sound  is  conducted 
to  the  ear  by  means  of  waves  which  are  transmitted  through  the  air 
or  through  other  material  substances. 

306.  Reflection  of  Sound.  —  Sound  waves,  like  other 
waves,  move  in  straight  lines  and  are  capable  of  reflection. 
The  echo  is  an  example  of  reflected  sound.  The  reflector 
is  usually  the  wall  of  a  house  or  a  cliff.  Generally 
speaking,  we  get  reflection  only  from  the  surfaces  of  large 
bodies.  The  dimensions  of  the  reflector  must  be  large  as 
compared  with  those  of  the  wave.  A  floating  block  upon 
water,  for  instance,  rides  upon  large  waves  without  divert- 
ing them  from  their  course,  but  it  reflects  small  ripples 
perfectly.  The  laws  of  reflection  are  much  more  easily 
studied  in  the  case  of  light.  They  will  be  discussed  in 
Chapter  XXXIX. 


VIBRATING  BODIES;    PITCH  AND   TIMBRE        341 


CHAPTER   XXXV 
VIBRATING  BODIES;    PITCH  AND  TIMBRE 

307.  Source  of   Sound  Waves.  —  Sound  is  produced  by 
the  periodic  vibration  of  bodies.     To  show  that  sounding 
bodies    are    actually 

in  a  state  of  move- 
ment, it  is  only  nec- 
essary to  mount  a 
ball  of  wood  or  cork, 
as  shown  in  Fig.  310, 
and  to  place  the 
same  in  contact  with 
one  prong  of  a  tun- 
ing fork,  or  with  the 

lip  of  a  bell.     If  we  

then  cause  the  tun- 
ing fork  or  bell  to 

resound  by  drawing  a  violin  bow  across  it,  the  suspended 
ball  will  be  driven  violently  from  its  position  by  the  move- 
ment of  the  vibrating  body. 

308.  Classification  of  the  Vibrating  Bodies  commonly  used 
in  Musical  Instruments.  —  The  sounds  employed  in  music 
are  commonly  produced  by  the  vibration  of  one  of  trie 
following  classes  of  bodies : 

(1)  Vibrating  plates.  The  most  important  instruments 
which  depend  upon  this  class  of  vibrations  are  drums, 
gongs,  cymbals,  etc. 


FIG.  310. 


342  THE  OUTLINES   OF  PHYSICS 

(2)  Vibrating  rods.    This  class  gives  us  the  tuning  fork, 
the  triangle,  the  reed,  etc. 

(3)  Vibrating  strings.     This  is  the  most  important  class 
of  all ;    to  it  belong  the  stringed  instruments,  such  as  the 
violin,  harp,  guitar,  zither,  piano. 

(4)  Vibrating  columns  of  air.     All  wind  instruments, 
including  the  human  voice,  belong  to  this  class. 

309.  Musical  Pitch.  —  That  property  of  sound  which 
depends  upon  the  rapidity  of  vibration  is  called  pitch. 
Pitch  is  stated  in  terms  of  the  number  of  vibrations  per 
second.  To  be  audible,  the  pitch  of  a  vibrating  body  must 
lie  between  certain  limits.  If  less  than  about  twenty-four 


FIG.  311.  FIG.  312. 


single  vibrations  per  second  take  place,  no  sound  is  heard. 
If  a  lath  be  clamped  to  the  table,  as  in  Fig.  311,  it  may 
be  made  to  vibrate  in  precisely  the  same  manner  as  a 
sounding  body ;  but  it  is  silent.  The  waves  which  it  sends 
forth  do  not  affect  the  ear.  We  say  that  its  pitch  is  below 
the  audible  limit.  If  the  tip  of  a  pencil  be  brought  lightly 
into  contact  with  the  free  end  of  the  rod,  it  will  be  found 
possible  to  count  the  separate  vibrations. 

The  upper  limit  of  audibility  is  tested  by  means  of 
small  steel  cylinders  mounted  as  in  Fig.  312.  These, 
tapped  with  a  mallet,  give  very  rapid  longitudinal  vibra- 
tions. The  power  of  hearing  the  tones  emitted  by  these 
bars,  the  pitch  of  which  rises  as  the  bars  grow  shorter, 


VIBRATING  BODIES  ;    PITCH  AND   TIMBRE        343 

varies  greatly.  Some  persons  can  hear  sounds  of  more 
than  32,000  vibrations;  in  most  cases,  audibility  ceases 
between  15,000  and  25,000  vibrations. 

To  illustrate  this  point,  procure  a  bar  of  tool  steel,  and 
have  two  cylinders  turned  from  it,  each  2  cm.  in  diameter. 
They  should  be  12-0  cm.  and  6*10  cm.  in  length.  They 
should  be  hardened  and  mounted  as  in  Fig.  312.  When 
tapped  on  the  end  with  a  wooden  mallet,  the  longer  cylin- 
der will  emit  a  high  but  audible  tone.  Very  few  persons 
will  be  able  to  hear  that  uttered  by  the  shorter  bar. 

310.  Musical  Tones  and  Noises.  —  All  bodies  vibrate  at 
a  period  which  is  natural  to  themselves,  and  depends  upon 
their  dimensions,  the  materials  of  which  they  are  made, 
and  their  structure.     Most  bodies,  however,  when  thrown 
into  motion  vibrate  not  as  a  whole,  but  independently,  in 
various  parts.      The  rates   of  vibration  of  these  various 
parts  are  not  necessarily  related  to  one  another  in  any 
simple  manner.     If  they  are  simply  related  to  one  another 
in  a  manner  which  will  be  discussed  later,  the  result  is 
what  we  call  a  musical  tone.      If  the  vibrations  of  the 
various  parts  are  not  thus  simply  related,  we  get  what  we 
term  a  noise.      The  only  distinction  between  noises  and 
musical  tones  is  that  the  former  are  of  a  complexity  which 
the  ear  is  unable  to  analyze.     This  difference  may  be  illus- 
trated by  means  of  the  sound  emitted  by  a  vibrating  plate, 
a  body  which  lies  upon  the  borderland  between  noise  and 
music.    The  method  described  in  the  following  experiment 
is  due  to  Chladni  (1756-1827),  a  celebrated  acoustician. 

311.  EXPERIMENT    98.  — The    Vibration    of    Plates;     Chladni's 
Figures. 

Apparatus : 

(1)  A  square  plate  of  sheet  brass,  which  should  be  as  nearly  per- 


344 


THE  OUTLINES   OF  PHYSICS 


fectly  flat  as  possible ;    it  should  be  about  30  cm.  square  and  0-3  cm. 
in  thickness.     Also  a  circular  brass  plate  of  the  same  diameter. 

(2)  A  large  clamp.     It  is  best  to  have  one  of  the  cast-iron  clamps 
which  are  made  purposely  for  this  experiment.     Any  clamp  of  size 
sufficient  to  reach  from  the  center  of  the  plates  to  the  edge  will  do  if 
provided  with  two  metal  buttons,  or  disks,  to  be  placed  between  the 
surface  of  the  plate  and  the  clamp,  at  the  center  of  the  former. 

(3)  An  ordinary  violin  or  bass-viol  bow. 

(4)  A  pepper  box  containing  dry  sand. 

Procedure : 

(a)  Clamp  the  square  plate  by  its  center.  Draw  the  bow  across 
its  edge,  and  note  the  character  of  the  sounds  which  it  may  be  made 
to  emit.  It  will  be  found  that,  while  they  are  not  altogether  devoid 
of  musical  character,  they  are,  for  the  most  part,  harsh  and  unpleas- 
ant. As  a  musical  instrument,  such  a  plate  would  be  held  distinctly 
inferior  to  any  stringed  instrument. 

(&)  The  vibrating  plate,  thus  set  in  motion,  resolves  itself  into  a 
considerable  number  of  vibrating  parts.  The  existence  of  these  may 
be  demonstrated  as  follows  : 

Strew  the  plate  with  sand  and  bow  it,  in  the  meantime  pressing 
the  tip  of  the  left  forefinger  against  one  edge.  Note  the  arrangement 
of  the  sand  particles  along  symmetrically 
situated  lines.  Make  free-hand  sketches 
of  the  patterns  thus  produced.  Figure  313 
shows  one  of  the  numerous  patterns  which 
may  be  obtained.  By  changing  the  posi- 
tion of  the  bow,  and  placing  the  finger  at 
various  points  upon  the  edge  of  the  vibrat- 
ing plate,  the  figures  produced  can  be  va- 
ried almost  indefinitely.  Chladni,  in  his 
work  on  "  Acoustics,"  depicted  several 
hundred  of  them.  Figure  314  is  reduced 
from  one  of  his  plates. 

The  lines  along  which  the  sand  settles 
when  the  plate  is  thrown  into  vibration 
are  lines  of  no  motion ;  they  divide  the 
plate  into  vibrating  parts.  These  lines  are  called  nodal  lines.  The 
vibrating  parts  of  the  body  are  called  segments. 

(c)   Repeat,  using  the  circular  plate.     Note  that  the  nodal  lines 


FIG.  313. 


VIBRATING  BODIES;    PITCH  AND   TIMBRE        345 


upon  the  circular  plate  are  equidistant  radii.     The  number  of  these 

determines  the  pitch  of  the  sound  which*  the  plate  emits.     In  order 

to  hold  these  lines  in  a  fixed 

position  upon  such  a  plate, 

it  is  necessary  to  check  the 

vibration 

upon  the 


at  some  point 
periphery  with 
the  finger,  and  the  plate 
then  divides  itself  into  an 
even  number  of  vibrating 
segments,  of  which  the 
usual  number  is  four. 

When  the  plate  is  thus 
divided  into  four  parts,  it 
utters  its  so-called  funda- 
mental tones.  When  more 
segments  are  produced, 
tones  of  higher  pitch  are 
the  result. 


312.  Vibration  of 
Bells.  —  The  case  of 
the  circular  plate  is  of 
interest,  because  its  mode  of  vibration  is  identical  with 
that  of  the  bell.  Bells,  whether  struck  with  the  clap- 
per or  set  into  vibration  by  means  of  the  bow,  vibrate 
thus  in  segments  separated  from  each  other  by  nodal  lines 
running  from  the  apex  to  the  lip  of  the  bell.  When  the 
bell  is  in  vibration  the  lip,  which  is  circular 
in  form  when  at  rest,  becomes  distorted  into 
the  form  of  an  ellipse.  (See  Fig.  315.) 
This  ellipse  changes  with  each  vibration. 
That  which  was  its  major  axis  at  one  instant 
becomes,  an  instant  later,  the  minor  axis. 
This  oscillation  takes  place  without  any 
movement  at  the  nodal  lines  which  pass  through  the  point 


FIG.  314. 


FIG.  315. 


346  THE  OUTLINES   OF  PHYSICS 

where  the  circle  and  the  two  ellipses  in  the  figure  cut 
each  other. 

The  vibration  of  the  bell  can  be  illustrated  by  nearly 
filling  a  light  glass  goblet  with  water.  If  the  finger  be 
placed  upon  the  edge  and  the  glass  be  thrown  into  vibra- 
tion with  the  bow,  there  will  be  four  regions  in  which  the 
water  will  remain  at  rest.  These  correspond  in  position 
to  the  nodal  lines.  Midway  between  these  nodes,  the 
water  will  be  thrown  into  violent  agitation 
and  its  surface  will  be  broken  up  into  a  series 
of  fine,  rapidly  moving  ripples.  (See  Fig. 
316.) 

It  was  noted  in  the  course  of  Experiment 
97  that  the  sounds  produced  by  the  vibration 
of  the  square  plate  were  decidedly  harsh  and 
unpleasant.  The  reason  for  this  lies  in  the 
fact  that  the  plate  breaks  up  into  so  many 

FIG.  316.  ...      .      „  ..  *  / 

dissimilar  segments,  all  of  which  vibrate 
simultaneously,  producing  sounds  which  do  not  necessarily 
harmonize.  The  vibrations  of  bells  are  simpler,  and  they 
therefore  fulfill  more  nearly  the  conditions  necessary  to 
the  production  of  a  musical  tone. 

313.  Tone-Color  or  Timbre.  —  Tone  color  is  the  property 
which  makes  it  possible  to  distinguish  between  sounds, 
even  when  they  have  the  same  pitch.  If,  for  example,  a 
cornet,  a  violin,  and  a  human  voice  are  sounding  the  same 
note  of  the  scale,  we  have  no  difficulty  in  telling  them 
apart.  Each  has  its  unmistakable  character,  due  to  the 
fact  that  it  is  really  a  composite  tone  produced  by  several 
independent  vibrations.  Such  tones  differ  from  musical 
chords  only  in  the  fact  that  one  of  the  vibrations  of  which 
they  are  composed  is  very  much  louder  than  the  others. 


VIBEATING  BODIES;    PITCH  AND   TIMBEE        347 

It  is  called  the  fundamental,  while  the  others  are  called 
overtones.  They  are,  as  a  rule,  scarcely  to  be  recognized 
individually ;  but  they  give  the  tone  its  color.  The  over- 
tones are  usually  due  to  the  vibration  of  smaller  segments 
of  the  same  body  which  produces  the  fundamental. 

A  good  example  of  color  tone  is  afforded  by  the  vowel 
sounds  u  (00),  0,  d',  a,  e.  If  these  be  sung  at  the  same 
pitch  their  fundamentals  are  identical,  but  each  possesses 
its  own  characteristic  set  of  overtones. 


348 


THE  OUTLINES   OF  PHYSICS 


CHAPTER   XXXVI 

EXPERIMENTS   WITH  TUNING  FORKS  ;    THE   MEASUREMENT 

OF  PITCH 

314.   The  Tuning  Fork.  —  This  instrument  consists  of  a 
stiff  rectangular  rod  of  steel  bent  upon  itself,  as  shown  in 
Fig.  317.     To  the  center  is  attached  a  handle,  or  shank, 
which  is  frequently  clamped  to   a 
sounding  box. 

The  sound  of  the  tuning  fork  is 
caused  by  the  simultaneous  vibra- 
tions of  the  two  prongs.  This 
motion,  which  is  too  rapid  to  mani- 
fest itself  directly  to  the  unaided 
eye,  can  be  made  easily  visible  in 
the  following  manner : 


FIG.  317. 


315.  EXPERIMENT  99.  —  Observation 
of  the  Motion  of  a  Tuning  Fork  by  Inter- 
rupted Vision. 

Apparatus : 

(1)  A  tuning  fork  (the  larger  the  better)  and  a  bow. 

(2)  A  disk  of  cardboard,  or  of  sheet  metal,  about  40  cm.  in  diam- 
eter.     It  should  contain  four  equidistant  radial  slots,  Fig.  318,  and 
should  be  mounted  to  revolve  upon  a  horizontal  axis  at  high  speed. 
A  convenient  form  for  this  apparatus  is  shown  in  the  figure.     It  con- 
sists simply  of  an  ordinary  "  whirling  table  "  clamped  in  a  vertical 
position. 

The  four  open  sectors,  or  slots,  should  be  about  1  cm.  wide  at  the 
periphery  of  the  disk. 


EXPERIMENTS    WITH  TUNING  FORKS 


349 


M  **O 


FIG.  318. 


Procedure : 

Set  the  tuning  fork  up  in  a  position  where  it  will  have  a  bright 
background,  or,  if  practicable,  the  sky  for  a  background.  In  front  of 
it,  at  a  distance  of  about  50  cm., 
mount  the  revolving  wheel.  Un- 
less the  wheel  is  to  be  driven 
automatically,  the  experiment 
should  be  performed  by  two  per- 
sons. The  tuning  fork  is  to  be 
kept  in  active  vibration  by  one 
of  the  operators ;  the  other  looks 
through  one  of  the  open  sectors 
of  the  disk  at  the  tuning  fork, 
then  starts  the  disk  into  motion. 
When  the  disk  has  reached  a 
speed  such  that  the  sensation  of 
flickering  has  vanished,  the  tun- 
ing fork  will  be  seen  as  if  by  con- 
tinuous vision. 

At  a  certain  speed  of  the  disk,  however,  the  tuning  fork  will  appear 
to  vibrate  very  slowly.     By  careful  adjustment  of  the  speed  it  may 
even  be  made  to  come  to  rest.     It  is  not  possible  to  drive  the  disk 
with  such  regularity  as  to  maintain  this  condition  of 
affairs,  but  it  is  easy  to  keep  the  apparent  motion  of  the 
tuning  fork  down  to  a  rate  such  as  to  enable  one  to  ex- 
amine the  character  of  the  motion  of  the  prongs. 

The  phenomena  observed  in  this  experiment  depend 
upon  persistence  of  vision.  The  observer  obtains  a  suc- 
cession of  views  of  the  tuning  fork ;  each  so  short  that 
the  fork  does  not  move  appreciably  before  the  light  is 
cut  off.  Each  successive,  instantaneous  view  shows  the 
fork  in  a  position  slightly  different  from  the  preceding 
one.  This  succession  of  views  overlaps  upon  the  retina 
and  is  blended  by  the  mechanism  of  vision  into  a  con- 
tinuous impression.  The  impression  produced  is  that  of 
a  fork  vibrating  with  a  very  slow  motion.  Note  that  the  amplitude 
of  vibration  of  the  tuning  fork  is  very  considerable  ;  the  prongs  being 
one  instant  spread  wide  apart  and  at  the  other  end  of  their  excursion 
being  bent  strongly  together  as  in  Fig.  319. 


FIG.  319. 


350 


THE  OUTLINES   OF  PHYSICS 


316.    EXPERIMENT  100.  —  Tuning  Fock  Tracings. 

Apparatus  : 

(1)  A  wooden  track  about  1  m.  long,  consisting  of  two  parallel 
guides  between  which  a  block  slides  smoothly. 

(2)  A  wooden  support  (S,  Fig.  320)  consisting  of  an  upright  piece, 


FIG.  320. 


20  cm.  square  and  2  cm.  in  thickness.     This  is  screwed  to  a  base  con- 
sisting of  two  blocks  hinged  together  as  shown  in  the  figure. 

(3)  Two  large  tuning  forks  and  a  bow. 

(4)  Several  pieces  of  glass  (cut  from  window  glass)  about  5  cm. 
wide  and  20  cm.  long. 

Procedure  : 

(a)  To  one  end  of  a  laboratory  table  clamp  the  support  S.  About 
12  cm.  above  the  table  bore  a  hole  through  the  upright  to  fit  the  shank 
of  the  tuning  forks.  Clamp  one  of  the  forks  to  the  support  by  slipping 
the  shank  through  the  hole  and  bolting  it  into  place  with  the  nut 
used  to  fasten  the  fork  to  its  sounding  box. 

(6)  From  a  bit  of  thin  sheet  metal,  ferrotype  iron,  or  copper  foil, 
cut  a  slender,  pointed  strip  about  4  crn.  long.  Bend 
this  strip  at  right  angles  as  in  Fig.  321,  and  fasten 
it  with  wax  to  one  prong  of  the  fork. 

(c)  Smoke  one  of  the  pieces  of  glass  over  a  candle 
flame,  and  fasten  it,  smoked  side  uppermost,  to  the 
FIG  321  sliding  block  by  means  of  thumb  tacks.     Place  the 

block  between  the  guides  of  the  wooden  track,  and 
adjust  the  latter  parallel  to  the  prongs  of  the  fork,  and  at  such  a 
height  below  it  that  when  the  block  is  at  one  end  of  the  track  the 


EXPERIMENTS    WITH  TUNING  FOBES.  351 

point  of  the  bent  strip  attached  to  the  prong  will  touch  the  smoked 
glass. 

(d)  Bring  the  fork  into  strong  vibration  by  lowering  it ;  then  draw 
the  block  from  under  it  by  means  of  a  string  previously  attached  to 
the  same.  The  motion  should  be  as  steady  as  possible,  with  a  velocity 
of  about  1  m.  per  second.  Note  that  the  tracing  is  sinusoidal,  like 
that  made  by  a  pendulum,  whence  it  follows  that  the  vibration  of  a 
tuning  fork  is  a  simple  harmonic  motion.  Figure  322  is  from  such  a 
tracing. 


FIG.  322. 

(e)  Repeat  the  experiment  with  two  forks.  The  second  fork 
should  be  mounted  by  means  of  another  hole  in  the  support,  so  placed 
that  the  two  forks  will  be  side  by  side  and  about  2  cm.  apart.  The 
stylus  on  each  should  be  on  the  inner  prong.  Compare  the  two  trac- 
ings obtained,  and  compute  from  them  the  relative  pitch  of  the  forks. 

Compare  the  ratio  obtained  from  your  measurements  with  that 
computed  from  the  rates  marked  upon  the  forks  by  the  maker. 

317.  Relative  and  Absolute  Pitch.  — The  foregoing  experi- 
ment illustrates  a  method  of  measuring  relative  pitch  of 
tuning  forks,  i.e.  of  obtaining  the  pitch  of  one  fork  as  com- 
pared with  that  of  another.     If   the  apparatus  were  so 
modified  as  to  permit  measurement  of  the  velocity  of  the 
plate,  the    absolute   pitch   could   be  determined.     To  get 
the  absolute  pitch  one  must  know  the  number  of  vibra- 
tions in  a  given  space  of  time.     If  the  distance  traversed 
by  the  plate  in  T^  second,  for  example,  were  known,  the 
absolute  pitch  would  be  determined  by  multiplying  the 
number  of  undulations  traced  within  that  distance  by  ten. 

318.  The  Method  of  Beats.  —  When  two  forks  or  other 
instruments  not  quite  in  unison  are  sounded  together,  a 
peculiar  throbbing   or   pulsating  effect  may  be   noticed. 


352 


THE  OUTLINES   OF  PHYSICS 


These  pulsations  are  called  beats.  The  more  closely  the 
forks  agree,  the  slower  are  the  beats.  When  complete 
unison  is  attained  they  disappear.  With  increasing  differ- 
ence of  pitch,  on  the  other  hand,  the  rapidity  of  the  beats 
increases  until  they  come  too  fast  to  be  distinguished. 
The  result  then  is  discord. 

Beats  are  due  to  the  fact  that  the  sound  waves  from 
the  two  instruments  combine ;  at  one  moment  to  reinforce, 
and  at  the  next  to  annul  each  other.  If,  for  example,  a 
tuning  fork  vibrates  255  times  a  second,  and  another  256 
times  a  second,  the  waves  from  them  will  reach  the  ear 
in  the  same  phase  once  every  second.  At  those  instants 
the  sounds  reinforce  each  other  and  give  us  beats.  The 
method  of  beats  consists  in  determining  when  two  instru- 
ments come  into  complete  unison  by  the  slowing  and  dis- 
appearance of  the  beats. 

319.  The  Graphical  Representation  of  Beats.  —  The  nature 
of  beats  may  be  shown  graphically  by  an  experiment  simi- 


FIG.  323. 


lar  to  that  described  in  Art.  316.  The  smoked  plate  is 
clamped  upon  one  of  the  forks,  as  shown  in  Fig.  323. 
Both  forks  are  set  in  motion,  and  the  tracing  is  made  by 
moving  one  of  them.  If  the  forks  are  nearly  in  unison, 


EXPERIMENTS   WITH  TUNING  -FORKS 


353 


the  tracing  will  present  an  appearance  like  that  shown  in 
Fig.  324.  The  experiment  should  only  be  tried  with  a 
fork  especially  constructed  to  carry  the  smoked  plate. 
The  latter  must  be  very  securely  clamped,  and  the  other 
prong  must  carry  a  counterbalancing  weight. 

320.  The  Optical  Study  of  Vibrations.  (Lissajous's  Method.) 

—  If  a  mirror  be  attached  to  a  tuning  fork,  and  a  beam  of 

light  from  a  lantern  be  reflected  thus  to  a  screen  (Fig. 

325),  an  image  of  a  small  aperture  may  be  focussed  upon 


FIG.  325. 


the  screen.  When  the  fork  vibrates,  this  image  will  be  drawn 
out  into  a  line  or  band.  When  viewed  in  a  revolving 
mirror  it  may  be  resolved  into  a  sinusoidal  curve.  With 


FIG.  326. 


2A 


354 


THE  OUTLINES   OF  PHYSICS 


two  forks,  each  provided  with  a  mirror  arranged  as  in 
Fig.  326,  movements  which  are  characteristic  of  the  com- 
bined vibrations  may  be  obtained.  With  parallel  vibra- 
tions the  foregoing  experiment  upon  beats  may  be  obtained. 
When  the  vibrations  are  perpendicular  to  one  another, 
certain  figures  are  obtained,  the  character  of  which  depends 
upon  the  ratio  of  pitch  of  the  forks  and  the  difference 
of  phase.  These  are  known  as  Lissajous's  figures.  Figure 
327  shows  some  of  the  most  important.  Lissajous's  figures 


1:1 


1:2 


1:3 


2:3 


FIG.  327. 


are  used  in  the  comparison  and  adjustment  of  tuning  forks. 
They  afford  one  of  the  most  delicate  methods  for  the  de- 
termination of  relative  pitch. 


THE   VIBRATION   OF  STRINGS  355 


CHAPTER   XXXVII 

THE   VIBRATION   OF   STRINGS 

321.  Modes  of  Vibration.  —  A  vibrating  string  is  always 
fixed  at  both  ends,  since  in  no  other  way  can  it  be  given  the 
necessary  tension.  It  vibrates  either  in  a  single  segment, 
or  vibrating  part,  or  is  broken  up  into  smaller  segments. 
These,  however  numerous  they  may  be,  are  always  simply 
related  as  to  their  length  and  rate  of  vibration  to  the  whole 
string ;  and  it  is  owing  to  this  simplicity  that  the  pleasant 
effects  of  vibrating  strings  are  due.  When  the  string  is 
vibrating  as  a  whole,  with  nodes  only  at  the  ends,  it  utters 
its  fundamental  tone,  which  is  the  lowest  tone  in  pitch 
the  string  can  be  made  to  produce.  If  the  center  of  the 
string  be  constrained  by  the  finger,  or  by  means  of  any 
stop,  the  string  will  vibrate  in  two  segments,  each  of 
which  is  half  the  length  of  the  entire  string,  and  each  of 
which  gives  forth  a  note  (the  octave),  the  vibration  period 
of  which  is  half  of  that  of  the  fundamental. 

By  placing  a  stop  at  the  distance  of  J  the  length  of  the 
string,  or  at  ^,  ^,  J,  -|-,  J-,  etc.,  of  that  length,  the  string 
may  be  broken  up  into  the  corresponding  number,  i.e.  3,  4, 
5,  6,  7,  or  8  vibrating  segments.  The  pitch  will  rise  in 
inverse  proportion  to  the  lengths  of  the  segments.  That 
the  vibrating  string,  when  thus  restrained  at  a  single  point, 
is  in  fact  broken  up  throughout  its  entire  length  into 
vibrating  segments  with  nodes  separating  them  which  are 
at  rest,  can  be  shown  as  follows : 


356 


THE   OUTLINES   OF  PHYSICS 


322.    EXPERIMENT  101.  —  Location  of   the   Nodes   in  a  Vibrating 
String. 

Apparatus : 

(1)  A  bow  and  rosin  ;  a  sheet  of  paper.     (Paper  which  is  colored 
upon  one  side  is  to  be  preferred.) 

(2)  A  sonometer.    The  sonometer  is  a  hollow  box  of  thin  spruce  or 
other  wood,  about  1  m.  long  and  30  cm.  wide.     (See  Fig.  328.)     This 


FIG.  328. 

box  carries  keys  at  either  end  by  means  of  which  strings  may  be 
stretched.  The  strings  pass  over  wedge-shaped  bridges,  so  that  they  all 
have  the  same  length.  Adjustable  bridges  also  are  provided,  by  means 
of  which  the  length  of  a  single  string  may  be  varied  at  will.  A  centi- 
meter scale  runs  the  length  of  the  sonometer,  dividing  the  distance 
between  the  bridges,  which  should  be  just  1  m.,  into  100  parts.  The 
construction  of  a  good  sonometer  is  a  task  requiring  something  of  the 
instrument  maker's  skill,  and  also  a  supply  of  properly  selected  and 
thoroughly  seasoned  wood.  For  the  following  experiment  a  dry 
board  of  pine  or  spruce,  rather  more  than  1  m.  long,  may  be  used  in- 
stead of  a  sonometer.  Across  this,  near  the  ends,  1  m.  apart,  V-shaped 
bridges  as  shown  in  the  figure  should  be  fastened.  An  ordinary 
meter  stick,  placed  with  its  ends  against  these  bridges,  will  serve  for 
a  scale.  To  one  end  of  this  improvised  sonometer  should  be  attached 
a  pair  of  pulleys,  over  which  the  wires  or  strings  to  be  experimented 
with  may  be  stretched  by  means  of  weights. 


THE  VIBRATION  OF  STRINGS  357 

Procedure  : 

(a)  Place  a  steel  wire  upon  the  sonometer,  and  increase  its  tension 
until  it  gives  a  distinct  musical  tone.  Place  the  finger  upon  the  mid- 
dle of  the  string,  and  bow  it  with  one  hand.  The  tone  now  emitted 
will  be  the  octave  of  the  fundamental.  That  both  ends  of  the  string 
are  thrown  into  vibration  may  be  shown  by  placing  a  small  rider  of 

paper,  in  the  form  shown  in  Fig.  329,  upon  the  uii-  

bowed  end  of  the  string,  anywhere  between  the 
finger  and  the  end.  This  will  be  thrown  off  as 
soon  as  the  bow  touches  the  other  half  of  the 

(6)  Move  the  finger  to  a  position  distant  one 

third  the  length  of  the  string  from  either  end.  Bow  the  short  portion 
of  the  string,  and  note  the  change  of  pitch.  There  will  now  be  a  node, 
or  point  of  rest,  midway  between  the  finger  and  the  further  end  of  the 
string.  To  locate  this,  place  at  the  point  in  question  one  of  the 
paper  riders  already  referred  to.  It  is  convenient  in  making  these 
riders  to  fold  one  set  of  them  with  the  white  and  the  other  with  the 
colored  side  out ;  and  to  use  the  white  riders  at  the  nodes,  the  colored 
ones  upon  the  vibrating  segment.  If  this  rider  be  properly  located, 
the  short  end  of  the  string  may  be  bowed  vigorously  without  displac- 
ing the  rider.  Other  riders  placed  anywhere  else  upon  the  intervening 
segments  of  the  string  will,  however,  be  thrown  off  at  once.  We  thus 
get  direct  ocular  evidence  that  the  string  is  vibrating  in  three  parts, 
although  only  one  of  these  is  directly  under  the  bow  ;  also,  that  there 
are  two  nodes  so  situated  as  to  divide  the  string  into  three  equal 
parts,  although  only  one  of  these  is  compelled  to  remain  at  rest  by  the 
presence  of  the  finger. 

(c)  Repeat  the  experiment  with  the  finger  one  fourth  the  length  of 
the  string  from  the  end.  Locate  two  other  nodes  and  show  that  they 
are  at  divisions  50  and  75  upon  the  scale.  Show  by  means  of  colored 
riders  that  the  four  intervening  portions  of  the  string  are  all  in  vibra- 
tion when  one  of  them  is  bowed.  Note  that  the  tone  emitted  by  the 
string  is  two  octaves  above  the  fundamental. 

323.  Motion  of  Bowed  String.  —  When  the  vibration  of 
a  string  is  not  hindered  by  a  stop,  it  is  possible  with  the 
bow  to  produce  vibrations  of  it  in  parts,  together  with  the 


358 


THE  OUTLINES   OF  PHYSICS 


fundamental  tone  of  the  string  vibrating  as  a  whole.  A 
single  string,  under  the  hands  of  a  skilled  performer,  is 
thus  made  to  utter  sounds  which  are  rich  in  tone  color ; 
and  it  is  to  these  that  the  beauty  of  the  music  of  stringed 
instruments  is  due. 

324.    EXPERIMENT  102.— Study  of  a  Bowed  String. 

Apparatus : 

(1)  A  violin  string  or  a  steel  wire,  tightly  stretched  horizontally 
between  wooden  supports. 

(2)  A  screen  with  a  narrow,  vertical  slit,  so  placed  in  front  of  the 
string  that  the  latter  will  bisect  the  slit. 

(3)  The  revolving  mirror  described  in  previous  experiments. 

(4)  A  bow,  rosin,  etc. 
Procedure : 

(a)  Mount  the  apparatus  so  that  the  string  will  be  strongly  illu- 
minated from  behind.  The  best  way  to  perform  the  experiment  is  to 
mount  the  string  in  the  field  of  the  lantern,  and  observe  its  projection 
upon  the  screen.  The  arrangement  of  the  apparatus  for  this  form  of 

the  experiment  is  shown  in 
Fig.  330.  In  front  of  the 
middle  of  the  string,  and 
not  more  than  2  cm.  from 
the  same,  set  up  the  slit, 
and  immediately  in  front 
of  that  the  revolving  mir- 
ror m,  so  placed  that  when 
it  is  at  rest  an  image  of  the 
slit  will  be  thrown  upon 
the  screen  S.  Upon  looking 
at  this  image,  one  will  see 
an  element  of  the  string  in 
the  form  of  a  short  black 

______^ line     bisecting     the     slit. 

FIG.  330.  "  When  the  string  is  plucked 

or  bowed,  this  black  line 

is  distended  into  a  band,  the  width  of  which  measures  the  amplitude 
of  vibration  of  that  portion  of  the  string.  If  the  revolving  mirror  is 


U 


STRING 


n 


THE   VIBEATION   OF  STEIN GS 


359 


turned,  the  image  of  the  slit  spreads  across  the  screen,  and  the  image 
of  the  string  forms  an  undulatory  line,  the  form  of  which  exhibits 
clearly  the  mode  of  vibration.  Projected  upon  the  screen,  this  ex- 
periment is  a  very  beautiful  one. 

(&)  Vary  the  action  of  the  bow,  and  note  the  changes  produced  in 
the  manner  of  vibration  of  the  string.  It  will  be  found  that  there 
are  three  prevailing  types  of  motion : 

1.  A  simple  sinuous  vibration  which  is  natural  to  a  freely  vibrat-    V 
ing  string  and  to  all  vibrating  bodies. 

2.  A  sinuous  vibration  with  more  rapid  motions  superimposed 
upon  it.     These,  which  are  due  to  overtones  of  the  string,  i.e.  to  the 
independent  vibration  of  small  segments  of  the  string,  are  superim- 
posed upon  the  larger  curve,  due  to  the  vibration  of  the  string  as  a 


vwwwwv 


FIG.  331. 


whole,  like  ripples  upon  a  wave.  The  third  type  is  produced  by  the 
action  of  the  bow  when  the  latter  clings  to  the  string,  only  partially 
releasing  it  from  moment  to  moment  and  then  seizing  it  again.  This 
produces  a  movement  of  the  string  which  is  forced.  It  is  represented 
by  a  series  of  oblique  straight  lines  instead  of  curves.  The  appear- 


360  THE  OUTLINES   OF  PHYSICS 

ance  is  that  of  a  succession  of  saw  teeth.  Messrs.  Raps  and  Menzel, 
in  Berlin,  have  photographed  a  great  number  of  these  types  of  vibra- 
tory motion.  Figure  331  is  reproduced  from  one  of  their  plates.  It 
shows  the  three  types  of  vibration  already  mentioned. 

This  experiment  serves  to  illustrate  the  fact  that,  under  the  action 
of  a  skilled  performer,  vibrating  strings  may  be  made  to  undergo  a 
great  variety  of  motions,  each  of  which  produces  its  characteristic 
effect  upon  the  ear.  It  is  to  this  variety  that  stringed  instruments, 
especially  those  in  which  the  bow  is  used,  owe  their  expression. 

325.  EXPERIMENT  103.  — Laws  of  the  Pitch  of  Vibrating  Strings. 
—  It  is  a  well-known  fact,  which  may  be  verified  by  a  moment's  ob- 
servation with  the  sonometer,  that  the  rapidity  of  vibration  of  a  string 
increases  with  the  tension,  and  that  it  increases  as  the  length  of  the 
string  is  diminished.  It  is  the  object  of  this  experiment  to  determine 
the  law  of  these  changes. 

Apparatus : 

(1)  A  sonometer,  some  pieces  of  steel  pianoforte  wire,  and  a  bow. 

(2)  A  clamp,  a  set  of  iron  kilogram  weights,  one  of  which  should 
be  provided  with  a  hook.     (See  Appendix  IV.) 

(3)  Three  tuning  forks  mounted  on  sounding  boxes ;  these  should 
give  the  tone  "ut2,"  "mi2,"  "so!2,"  or  the  corresponding  tones  of  the 
next  higher  octave.1 

Procedure : 

(a)  Mount  a  fine  steel  wire  upon  the  sonometer,  fastening  it  at 
one  end  and  carrying  the  free  end  over  the  pulley.  Clamp  the 
sonometer  firmly  to  the  table,  with  the  end  which  carries  the  pulleys 
projecting  over  the  edge.  Hang  weights  to  the  free  end  of  the  wire, 
testing  its  pitch  from  time  to  time,  until  its  sound  approaches  unison 
with  that  of  the  "  ut "  fork.  Make  careful  adjustments  of  the  weights, 
using  the  tenths  of  kilograms  until  the  agreement  is  as  good  as  you 
can  get.  Note  the  amount  of  weight  applied,  the  length  of  the  wire, 
and  its  diameter. 

(J)  Add  more  weights  until  the  wire  comes  into  unison  with  the 
"mi"  fork.  Note  the  amount  necessary  to  bring  this  about,  and 
repeat,  using  the  "  sol "  fork.  Tabulate  your  results  as  follows  : 

1  The  mark  "ut"  upon  an  instrument  indicates  pitch  corresponding 
to  "  do  "  or  C  of  the  English  notation. 


THE  VIBRATION  OF  STRINGS 


361 


TABLE. 

PITCH  AND  TENSION  OP  A  STEEL  WIRE. 
Diameter  of  wire,  0-025  cm.     Length,  50  cm. 


Pitch 

Weight  applied  =  M 

SM 
Pitch 

Utz  =512s.v. 

Mis  =  640  s.v. 
Sols  =  768  s.v. 

2800  g. 
4200  g. 
6430  g. 

0-1033 
0-1012 
0-1045 

3)  -3090 
Aver.  =  -103 

It  is  a  well-established  law  of  vibrating  strings  that  the  pitch  will 
be  directly  proportional  to  the  square  of  the  weight  applied.  Test 
the  accuracy  of  your  determinations  by  dividing  the  square  root  of 
each  weight  in  grams  by  the  number  of  single  vibrations  made  by  the 
fork  with  which  in  each  case  the  pitch  of  the  string  was  compared 
as  a  standard :  this  ratio  should  be  constant. 

(c)  Restore  the  stretching  weight  to  the  value  necessary  to  give 
the  tone  "  ut2 "  by  comparison  with  the  fork.     Leaving  this  weight 
constant,  insert  a  temporary  bridge  under  the  stretched  wire,  and  slide 
it  along  the  length  of  the  wire  until  the  pitch  of  the  longer  portion 
of  the  string  coincides  successively  with  that  of  the  "  mi "  fork  and 
the  "sol"  fork.      Note  the  position  of  the  bridge  when  the  string 
comes  into  unison  with  each  of  these  forks.     Your  readings  should 
show  that  the  pitch  of  a  string  under  constant  tension  varies  inversely  as 
the  length. 

(d)  Stretch  side  by  side  with  the  wire  thus  far  used,  one  of  greater 
diameter.     Add  weights  to  the  latter  until  it  also  comes  into  unison 
with  the  "  ut2 "  fork.     Continue  the  adjustment  until  the  strings  are 
in  unison  with  one  another  and  also  with  the  fork.     Measure  the 
diameter  of  the  larger  string,  and  read  the  weights  attached  to  each. 
Compute  the  relative  areas  of  cross-section  of  the  two  wires,  and  see 
in  how  far  your  observation  verifies  the  law  that  strings  of  the  same 
material  and  the  same  length  vibrate  at  .the  same  pitch  when  the 
stretching  weights  are  proportional  to  the  cross-section. 

[If  more  convenient,  the  larger  string  may  be  stretched  in  place  of 
the  smaller  one,  and  tuned  by  reference  to  the  fork.] 


362  THE  OUTLINES   OF  PHYSICS 


CHAPTER   XXXVIII 
WIND  INSTRUMENTS  AND  RESONATORS 

326.  The  Vibration  of  Air  Columns.  —  In  wind  instru- 
ments, the  vibrating  body  is  a  column  of  air. 

The  visible  instrument  serves  simply  to  fix  the  size  of 
the  air  column.  The  vibrations  of  the  latter  give  the 
pitch,  those  of  the  wooden  or  metal  walls  affect  only  the 
timbre. 

The  vibration  of  an  inclosed  air  column  may  be  excited 
in  a  variety  of  ways.  If,  for  example,  the  end  of  an 
argand  lamp  chimney,  or  any  open  tube,  be  struck  with 
the  palm  of  the  hand,  it  will  utter  a  musical  tone  due 
to  the  vibration  of  the  inclosed  column  of  air.  If  the 
hand  be  pressed  against  the  end  of  the  tube  and  suddenly 
removed,  a  faint  tone  will  likewise  be  heard  which  is  the 
octave  above  that  obtained  by  closing  the  end.  The  chim- 
ney when  closed  with  the  hand  forms  what  is  known  as 
a  closed  pipe.  When  both  ends  are  open  it  is  an  open  pipe. 
The  fundamental  tone  of  a  closed  pipe  is  an  octave  below 
that  of  an  open  pipe  of  the  same  size. 

To  maintain  the  sound  of  a  pipe,  what  is  called  a 
standing  wave  must  be  produced.  In  other  words,  the 
air  column  must  be  made  to  vibrate  longitudinally  with 
a  motion  like  the  longitudinal  vibration  of  a  solid  bar. 
This  condition  may  be  produced  by  the  motion  of  a  solid, 
the  pitch  of  which  corresponds  with  that  of  the  air  column, 
as  shown  in  the  following  experiment: 


WIND  INSTRUMENTS  AND  RESONATORS 


327.    EXPERIMENT  104.  —  Resonance  of  an  Air  Column  excited  by 
a  Tuning  Fork. 
Apparatus : 

(1)  A  tuning  fork  and  bow. 

(2)  A  tall  cylindrical  vessel  of  glass. 

(3)  A  beaker  or  flask  filled  with  water. 
Procedure : 

(a)  Put  the  tuning  fork  into  vibration  and  hold  it  over  the  mouth 
of  the  cylinder. 

Pour  water  into  the  latter  slowly  from  the  flask.  Note  that  when 
the  water  reaches  a  certain  level,  the  cylinder  emits  a  strong  musical 
tone,  agreeing  in  pitch  with  the  tuning  fork ;  and  that  this  tone  dies 
away  again  as  the  level  rises.  This  observation  indicates  that  the 
tuning  fork  is  capable  of  exciting  only  a  column  of  certain  length, 
and  that  the  fundamental  tone  of  the  latter  has  the  same  pitch  as 
the  fork. 

(&)  Repeat  the  above  operation,  ceasing  to  add  water  when  the 
tone  of  the  cylinder  is  loudest.  Measure  the  length  of  the  air 
column  from  the  mouth  of  the  cylinder  to  the  surface  of  the  liquid. 
Note  the  pitch  (in  single  vibrations)  marked  upon  the  shank  of  the 
fork. 

Since  a  tuning  fork  sends  forth  one  wave  in  the  air  for  each  com- 
plete (or  double)  vibration,  we  can  compute  the  distance  between 
successive    waves,    and    compare    this    wave 
length  with  the  length  of  the   vibrating   air 
column.     For  example,  with  a  fork  marked 
512   s.v.,   256    waves    will    be  started  every 
second.     The  velocity  of  sound  is  33300  cm., 
and  these  waves  are  therefore  33300-130+  cm. 
apart. 

The  wave  length  130  cm.  is  that  of  the 
fundamental  tone  of  the  fork,  and  likewise 
of    the    air   column   which    responds    to    it. 
Measurement  of  the  length  of  the  latter,  how- 
ever, will  give  about  32-5  cm.  =  if£.     .•.  The  _ 
fundamental  wave  of  a  closed  pipe  is  four  times  -pIG   332 
the  length  of  the  pipe. 

(c)  The  sound  waves  produced  by  the  two  prongs  of  the  fork 
interfere,  and  tend  to  a  certain  extent  to  neutralize  each  other.  The 


364  THE  OUTLINES   OF  PHYSICS 

resonance  of  the  cylinder  will  therefore  be  more  intense  when  the 
wave  from  one  prong  is  suppressed.  To  verify  this  statement, 
roll  a  piece  of  paper  into  the  form  of  a  tube  large  enough  to  inclose 
one  prong  of  the  fork  without  touching  it.  Hold  the  vibrating  fork 
above  the  mouth  of  the  cylinder  as  in  Fig.  332.  Slip  the  paper 
tube  over  the  upper  prong  of  the  fork,  and  withdraw  it  several  times, 
noting  the  successive  accessions  and  diminutions  of  loudness  thus 
produced. 

328.  Resonators.  —  An  air  column  adjusted  so  as  to 
vibrate  in  unison  with  a  sounding  body,  and  to  reinforce 
the  tone  of  the  latter,  is  called  a  resonator.  The  glass 
cylinder  in  the  foregoing  experiment,  for  example,  is  a 
resonator;  the  sounding  boxes,  upon  which  tuning  forks 
are  mounted,  also  the  sounding  boards  of  pianos  and  the 
bodies  of  violins,  etc.,  are  resonators.  Every  inclosed 
body  of  air  acts  as  a  resonator  to  some  particular  wave 
length.  Thus  it  is  that  a  seashell,  or  other  hollow  body, 
held  to  the  ear,  murmurs  continually.  The  outer  air  is 
crowded  with  sound  waves,  which  constitute  the  volume 
of  ever-present  noise.  The  resonator  responds  only  to 
the  single  wave  length  with  which 'it  is  in  tune. 

By  means  of  a  set  of  resonators  corresponding  to  the 
various  tones  used  in  music,  it  is  possible  to  detect  the 
various  vibrations  contained  in  sounds  far  too  complex 

to  be  analyzed  by  the  unaided  ear 

and   to   express   them   in  musical 

notation. 

Such     resonators     are     usually 

given  the  form  shown  in  Fig.  333. 

FIG    333 

Two   brass    cylinders,    one   partly 

closed,  the  other  drawn  out  conically  to  a  small  open  tip 
which  fits  the  ear,  slide  one  within  the  other. 

The  length  is  thus  adjustable,  and  the  resonator  will 


WIND  INSTRUMENTS  AND  RESONATORS 


365 


respond,  according  to  its  length,  to  any  single  tone  within 
a  range  of  several  whole  tones  of  the  scale. 

By  means  of  sets  of  such  resonators,  many  interesting 
analyses  of  complex  sounds  have  been  made.  The  various 
tones  which  make  up  the  roar  of  Niagara,  for  example, 
have  been  isolated,  and  written  down  in  the  form  of  a 
complex  chord. 

329.  Essential  Parts   of   a   Musical   Instrument.  —  It   is 
obvious,  from  the  preceding  articles,  that  a  musical  in- 
strument has  two  essential  parts:    (1)   a  vibrating  solid, 
the  motion  of  which  determines  the  pitch ;   (2)  a  resonator 
which  reinforces  the  sound,  and  gives  volume  and  charac- 
ter to  the  instrument.     In  wind  instruments,  the  vibrating 
solid  is  a  less  conspicuous  part  than  in  stringed  instru- 
ments.    In  the  voice,  the  vocal  chords  play  this  essential 
part ;   in  reed  instruments,  a  small  tongue  of  sheet  metal 
(the  reed)  in  the  mouthpiece ;  while,  in  some 
instruments,  the  lips  of  the  performer  are  the 
vibrating  solids. 

330.  The  Organ  Pipe.  —  This  is  the  simplest 
type  of   wind   instrument.      It    consists  of   a 
long,  hollow  box  or  tube  (Fig.  334),  generally 
of  wood,  and  of  rectangular  cross-section.     It 
is    sometimes    open    at    both   ends  (an   open 
pipe)  ;  sometimes  one  end  is  closed  (a  closed 
pipe).      The   draught   of   air  blown   through 
the  mouthpiece  is  projected  against  the  sharp, 
wedge-shaped  lip  Z,  and  is  thrown  into  violent 
oscillations.     The    effect   is   similar  to  that  produced  by 
blowing  sharply  against  the  edge  of  a  piece  of  cardboard. 
Of  the  numerous  waves  thus  produced,  those  which  are  of 


FIG.  334. 


366  THE  OUTLINES   OF  PHYSICS 

the  proper  pitch  are  reinforced  by  the  air  column  within 
the  pipe,  which  acts  as  a  resonator. 

When  the  air  within  the  organ  pipe  is  thrown  into  vibra- 
tion by  the  action  of  the  mouthpiece,  a  sound  wave  travels 
the  length  of  the  pipe,  to  the  further  end,  where  it  is  re- 
flected and  returns  upon  its  course.  If  a  second  wave  fol- 
lows the  first  one  after  the  proper  interval,  a  standing  wave 
is  formed,  and  the  tone  is  maintained.  If  this  wave  has  a 
wave  length  equal  to  four  times  the  length  of  the  pipe, 
for  a  closed  pipe,  the  tone  which  is  produced  is  called  the 
fundamental  tone.  If  twice  as  many  waves  per  second  be 
started  at  the  mouthpiece,  the  octave  of  the  fundamental 
will  be  produced;  and  if  Avaves  be  started  still  more 
rapidly,  other  overtones  corresponding  to  the  overtones  or 
harmonics  of  a  vibrating  string  will  be  formed.  In  an 
open  pipe,  the  fundamental  tone  has  a  wave  length  which 
is  only  twice  as  long  as  the  pipe  itself,  and  which  is,  there- 
fore, an  octave  higher  than  that  of  the  closed  pipe. 

The  pitch  of  an  organ  pipe  depends  upon  the  length  of 
time  required  for  a  sound  wave  to  travel  from  the  mouth- 
piece to  the  further  end  of  the  pipe  and  back  again.  If 
the  pipe  be  filled  with  some  gas  in  which  sound  travels 
more  rapidly  than  in  air,  the  pitch  will  be  raised  in  pro- 
portion to  the  increase  of  velocity.  This  statement  may 
be  verified  as  follows : 

331.  EXPERIMENT  105.  —  Pitch  of  an  Organ  Pipe  when  filled  with 
Illuminating  Gas. 

Apparatus : 

An  organ  pipe  and  a  retort  stand. 

Procedure : 

Support  a  closed  pipe  in  a  vertical  position,  as  shown  in  Fig.  335. 
By  means  of  a  rubber  tube  connected  with  the  gas  mains,  fill  the  pipe 
with  illuminating  gas,  and  withdraw  the  tube.  Sound  the  pipe  at 


WIND  INSTRUMENTS  AND  RESONATORS          367 

once,  and  notice  that  the  pitch  grows  lower  as  the  gas  is  supplanted 
by  atmospheric  air.     By  the  use  of  hydrogen,  in  which  sound  travels 
much  more  rapidly  than  in  the  mixture  used 
for  illuminating  purposes,  the  effect  is  still  more 
marked. 


H 


332.  Influence  of  Temperature  upon  the 
Pitch  of  an  Organ  Pipe.  —  Since  the  ve- 
locity of  sound  in  air  rises  with  the  tem- 
perature, it  follows  that  a  pipe  filled  with 
hot  air  will  have  a  higher  pitch  than  if 
the    air   were  at  a  lower    temperature. 
This  may  be  shown  by  the  introduction 
of  a  lighted  candle  into  an  organ  pipe 
which  is  mounted  vertically.    The  change 
of  pitch  of  the  pipe  can  be  most  easily 
detected  in  this  by  comparing  it  with  a 
second    instrument,    with   which,   when 

cold,  it  is  in  unison.  FlG'  335< 

333.  Overtones  in  Wind  Instruments.  —  The  shrill  over- 
tones which  are  produced  by  a  powerful  blowing  of  wind 
instruments  are  due  to  the  breaking  up  of  the  air  column 
into  numerous  short  standing  waves.      The  presence  of 
these   may  be   illustrated   by  adjusting  to  any  ordinary 
whistle,  the  end  of  which  is  left  open,  a  glass  tube  about 
1  m.  in  length,  and  2  or  3  cm.  in  diameter.     If  a  small 


FIG.  336. 

quantity  of  lycopodium  powder  be  introduced  into  this 
tube,  and  distributed  throughout  its  length,  and  if  the 
tube  be  then  placed  horizontally,  and  be  strongly  blown 


368 


THE  OUTLINES   OF  PHYSICS 


for  an  instant,  it  will  be  found  that  the  dust  tends  to 
arrange  itself  in  the  form  of  equidistant  transverse  ridges. 
These  ridges  lie  in  the  nodes  of  the  wave.  (See  Fig.  336.) 

334.  The  Manometric  Flame.  —  This  is  an  ingenious  de- 
vice for  studying  the  vibrations  in  organ  pipes  and  other 
wind  instruments.  An  opening  in  the  wall 
of  the  pipe  (Fig.  337)  is  closed  with  a 
flexible  diaphragm  over  which  is  a  hollow 
chamber  R.  This  is  connected  with  the 
gas  main  through  a  tube  g,  and  with  a 
small  circular  gas  jet  through  another 
tube  t. 

Changes  of  pressure  within  the  organ 
pipe  are  transmitted  through  the  diaphragm 
to  the  gas  in  R,  and  thence  to  the  jet. 
The  flame  dances  in  time  with  the  vibra- 
tion within  the  pipe,  and  its  image,  viewed 
in  a  revolving  mirror,  appears  as  in  Fig.  338. 


u\\v\v\\v 


FIG.  338. 


335.   EXPERIMENT   106.  —  Analysis  of   Speech  by  Means  of   the 
Manometric  Flame. 

Apparatus : 

(1)  A  manometric  flame  apparatus  of  the  form  shown  in  Fig.  339. 


WIND  INSTRUMENTS  AND  RESONATORS 


369 


This  consists- of  an  argand  chimney,  to  one  end  of  which  a  cork  is 
fitted.  Through  this 
cork  two  glass  tubes 
pass,  one  of  which  is 
connected  with  the 
gas,  the  other  with  a 
jet  made  by  drawing 
a  glass  tube  down  to 
about  0-1  cm.  diam- 
eter. Over  the  other 
end  of  the  chimney  is 
stretched  a  piece  of 
the  thinnest  obtain- 
able sheet  rubber.  A 
conical  mouthpiece  of 
pasteboard  completes 
the  instrument. 

(2)   A  revolving 
mirror. 

Procedure : 

(a)  Turn  on  the  gas,  light  the  jet,  and  adjust  to  a  flame  height  of 
about  2  cm. 

(&)  Speak  or  sing  into  the  mouthpiece,  watching  the  flame  mean- 
time in  the  revolving  mirror.  Observe  the  forms  of  the  serrated 
image  corresponding  to  various  articulate  sounds,  particularly  to  syl- 
lables containing  hissing  or  explosive  elements,  />,  pr,  t,  s,  etc.,  and  to 
the  vowels,  a,  a,  e,  o,  ou,  etc. 

Figure  340  shows  the  image  produced  by  the  word  INK. 


FIG.  339. 


FIG.  340. 


PART  V-  -LIGHT 


CHAPTER   XXXIX 

REFLECTION  AND   REFRACTION 

336.  The  Propagation  of  Light.  —  Light,  like  sound,  is 
propagated  by  means  of  a  wave  motion,  but  light  waves 
differ  from  sound  waves  in  many  respects.  The  velocity 
is  much  greater,  as  has  been  already  pointed  out  in  Chap- 
ter XXXIII.  A  light  wave  travels  from  the  sun  to  the 
earth,  for  example,  in  eight  minutes,  which  requires  a 
velocity  of  over  300,000,000  of  meters  per  second.  A 


REVOLVING  MIRROR  FIXED  MIRaOR. 

FIG.  341. 

sound  wave,  which  travels  in  air  332  m.  per  second,  would 
take  nearly  fourteen  years  to  traverse  the  same  space. 

Enormous  as  the  velocity  of  light  is,  it  has  been  found 
possible  to  measure  it  experimentally.  A  small  mirror  n 
(Fig.  341)  is  made  to  revolve  several  hundred  times  per 
second.  A  ray  of  sunlight  reflected  from  it  to  a  second 
mirror  m  (situated  at  a  considerable  distance),  and  back 
again,  is  found  to  take  a  slightly  different  course  when 

370 


REFLECTION  AND  REFRACTION 


371 


reflected  the  second  time.  The  mirror  has  had  time  to 
revolve  through  a  small  angle  while  the  ray  was  traveling 
to  the  fixed  mirror  and  back  again.  By  measuring  this 
minute  angle  and  the  distance  between  the  mirrors,  the 
velocity  of  light  has  been  found  to  be  300,574,000  m. 
(186,680  miles)  per  second. 

Light  waves  differ  from  sound  waves  also  as  to 
wave  length  and  frequency.  The  sound  waves  used  in 
music  have  wave  lengths  lying  between  16  feet  and  3 
inches.  The  number  of  vibrations  varies  between  about 
32  and  4000  vibrations  per  second.  The  light  waves  to 
which  the  eye  is  sensitive  have  wave  lengths  lying  be- 
tween 0-000076  and  0-000039  cm. ;  they  oscillate  between 
392,000,000,000,000  and  about  757,000,000,000,000  times 
per  second.  Sound  waves  in  air  consist  of  longitudinal 
vibrations.  Light  is  due  to  the  transverse  vibration  of  an 
imponderable  medium  which  is  supposed  to  fill  all  space, 
and  which  is  called  the  luminiferous  ether. 

337.  Reflection  of  Light.  —  The  law  of  reflection  of  light 
is   usually  stated   thus:     The  angle 

of  incidence  is  equal  to  the  angle  of 
reflection.  These  angles,  which  are 
marked  i  and  r  in  Fig.  342,  are  the 
angles  between  a  line  drawn  normal 
to  the  reflecting  surface,  and  the 
directions  of  the  incident  and  the  ,-- 
reflected  ray  respectively.  This  law 
may  be  verified  as  follows  : 

338.  EXPERIMENT  107.  —  Equality  of  the  Angles  of  Incidence  and 
Reflection. 

Apparatus : 

An  ordinary  plane  mirror,  to  the  frame  of  which  a  wooden  pointer 
has  been  attached  at  right  angles  to  the  reflecting  surface. 


SURFACE 

FIG.  342. 


372 


THE  OUTLINES   OF  PHYSICS 


Procedure : 

(a)  Mount  the  mirror  in  a  darkened  room  with  freedom  of  rota- 
tion upon  a  horizontal  axis.  (See  Fig.  343.)  Send  a  beam  of  hori- 
zontal light  to  the  mirror  from  a  projecting  lantern  or  from  a  porte 
lumiere1  placed  outside  the  room  and  reflecting  the  sun's  rays  in 
through  a  hole  in  the  shutter. 

(6)  Rock  the  mirror  to  and  fro  upon  its  axis,  and  notice  that  the 
pointer  always  bisects  the  angle  between  the  incident  and  the  reflected 
ray.  The  path  of  these  rays  may  be  rendered  more  easily  visible  by 
filling  the  air  in  front  of  the  mirror  with  chalk  dust. 


FIG.  343. 


FIG.  344. 


339.  Position  of  the  Image  behind  a  Plane  Mirror.  —  The 

image  formed  by  a  plane  mirror  is  of  the  same  size  as  the 
object,  and  its  distance  behind  the  mirror  is  the  same  as 
that  of  the  object  in  front  of  the  latter.  The  line  joining 

1  Porte  lumiere :  an  arrangement  for  introducing  a  horizontal  ray  of 
sunlight  into  a  darkened  room.  It  consists  of  an  adjustable  mirror  placed 
outside  of  the  window  shutter.  Such  mirrors  are  mounted  so  as  to  have 
a  freedom  of  motion  upon  two  axes,  one  of  which  should  be  parallel  to 
the  polar  axis  of  the  earth.  -When  driven  by  clockwork,  so  as  to  main- 
tain the  reflected  ray  constantly  in  a  fixed  position  in  spite  of  the  motion 
of  the  earth,  the  instrument  is  called  a  heliostat. 


REFLECTION  AND  REFRACTION  373 

a  given  point  in  the  object  and  the  image  of  that  point  is 
bisected  by  the  mirror,  and  is  perpendicular  to  the  surface 
of  the  same.  To  an  observer  looking  towards  a  plane 
mirror  the  image  appears  in  the  direction  of  the  ray  from 
the  face  of  the  mirror  to  his  eye.  The  position  of  the 
image  is  found  by  turning  the  reflected  ray  r  (Fig.  344) 
until  it  coincides  in  direction  with  the  incident  ray  i ;  i.e. 
into  the  position  r'  behind  the  mirror.  The  sum  of  the 
distances  i  +  r  will  be  the  same  as  i  +  r1.  The  image  will 
therefore  be  as  far  behind  the  mirror  as  the  object  is  in 
front  of  it. 

340.  Concave  and  Convex  Mirrors.  —  In  the  case  of  curved 
surfaces,  although  the  law  of  reflection  is  the  same  for  each 
point  of  the  surface,  as  in  the  case  of  plane  mirrors,  the 
results  produced  are  very  different.  The  most  important 
case  is  that  of  the  concave  mirror.  This  has  a  surface 
which  is  a  portion  of  the  inner  surface  of  a  sphere. 


FIG.  345. 


(1)  Consider  the  rays  of  light  from  a  point  a  in  front 
of  the  mirror.  Those  which  reach  the  surface  of  the 
mirror  are  reflected,  each  one  in  accordance  with  the  law 
of  reflection  given  in  the  foregoing  article.  As  will  be 
seen  from  Fig.  345,  all  these  rays  come  together  at  a 


374  THE  OUTLINES   OF  PHYSICS 

single  point  b  in  front  of  the  mirror.  If,  on  the  other 
hand,  the  source  of  light  were  situated  at  ft,  rays  emanat- 
ing from  it,  and  reaching  the  mirror,  would  all  be  reflected 
to  a.  The  points  a  and  b  are  called  conjugate  foci. 

(2)  If  the  source  of  light  be  situated  at  the  center  of 
the  mirror  (7,  the  angles  of  incidence  arid  reflection  are 
reduced  to  zero.     Since  all  rays  strike  the  surface  of  the 
mirror  normally,  they  will  be  reflected  directly  back  upon 
their  course,  and  will  be  brought  to  a  focus  at  0. 

(3)  Consider  the  rays  from  a  point  F  halfway  between 
the  center  of  the  mirror  and  its  surface  (Fig.  346).     The 

reflected  rays  will  be  every- 

where  parallel   to   the  axis 

of   the    mirror.      They  can 
~-^  be    considered    as    meeting 

F  ^-'"  C  only  in  infinity.     If  parallel 

rays,    namely,    tho'se    from 
some    very   distant    source, 
FIG  ^g  such  as  the  sun  or  a  fixed 

star,  fall  upon  the   mirror, 

the  latter  being  placed  so  that  its  axis  is  parallel  to 
the  rays,  they  will  come  together  at  the  point  F  which, 
as  above  stated,  is  halfway  between  the  surface  of  the  * 
mirror  and  its  center  of  curvature.  This  point  at  which 
parallel  rays  are  brought  to  a  focus  is  called  the  principal 
focus  of  the  mirror. 

341.  -Real  and  Virtual  Images.  —  Consider  a  candle  G^G^ 
in  front  of  a  concave  mirror.  The  rays  from  each  portion 
of  it,  after  reflection  from  the  face  of  the  mirror,  will  be 
brought  to  a  focus  at  some  given  point.  Thus  the  rays 
from  the  tip  of  the  candle  at  C1  (Fig.  347)  will'  come  to 
a  focus  at  c± ;  those  from  the  base  of  the  candle  O.2  at  c2. 


\ 


REFLECTION  AND  REFRACTION 


375 


Intermediate  points  in  the  object  will  come  to  a  focus 
at  points  lying  between  these  two.  These  various  foci  of 
light  reflected  from  the  surface  of  the  candle  produce  an 


Ci 


FIG.  347. 


image  of  the  candle.  This  image,  unlike  the  image  in  the 
plane  mirror,  is  in  front  of  the  mirror.  It  is  not,  generally 
speaking,  of  the  same  size  as  the  candle  itself.  It  is 
inverted  instead  of  being  erect.  Images  thus  formed  by 
means  of  a  concave  mirror  are  called  real  images.  They 
differ  from  images  behind  the  mirror,  which  are  called,  to 
distinguish  them,  virtual  images,  in  one  important  particu- 
lar. The  rays  are  actually  present  where  the  real  image 
is  formed ;  they  only  appear  to  pass  through  the  position 
of  the  virtual  image. 

In  order  that  a  real  image  may  be  formed  by  means  of 
a  concave  mirror,  the  object  must  be  placed  beyond  the 
principal  focusi  The  rays  from  an  object  situated  between 
the  princip&Lfocus  and  the  mirror  itself  will  not  converge 
to  any  focus  in  front  of  the  mirror  after  reflection,  but  will 
diverge,  as  shown  in  Fig.  348.  These  divergent  rays,  if 
we  imagine  them  produced  behind  the  mirror,  will,  how- 
ever, come  to  focus  so  as  to  form  a  virtual  image  at  i. 
This  image,  like  the  image  in  the  plane  mirror,  will  be 
erect,  but  its  size  is  not  the  same  as  that  of  the  object, 


376 


THE  OUTLINES   OF  PHYSICS 


nor  is  it  situated  the  same  distance  behind  the  mirror  that 
the  object  is  in  front.     Its  size  and  position,  which  vary, 


0      F     ^-~"  C 


FIG.  348. 


may  be  determined  from  the  direction  of  the  reflected 
rays.  The  intersection  of  the  paths  of  these  behind  the 
mirror  indicate  the  position  of  the  image. 


FIG.  349. 


The  images  produced  in  convex  mirrors  are  always 
virtual,  since  the  reflected  rays  from  any  object  in  front 
of  the  mirror  will  diverge.  (See  Fig.  349.) 


EEFLECTION  AND  REFRACTION 


377 


The  convex  mirror  has  no  very  important  application  in 
optics,  but  concave  mirrors  are  much  used.  In  reflecting 
telescopes,  real  images  of  stars  and  other  distant  objects, 
formed  by  the  use  of  such  a  mirror,  are  magnified  by 
observing  it  through  an  eyepiece.  The  largest  telescopes 
ever  constructed  have  been  of  this  kind.  The  great 
reflecting  telescope  of  Lord  Rosse,  the  mirror  of  which 
was  six  feet  in  diameter,  is  shown  in  Fig.  350. 


FIG.  350. 

342.  Refraction.  —  When  a  ray  of  light  falls  upon  any 
surface,  a  portion  of  the  ray  penetrates  the  body.  If  the 
latter  be  transparent,  this  portion  of  the  ray  will  be  trans- 
mitted; if  the  body  be  opaque,  the  wave  motion  will  be 
destroyed  and  its  energy  converted  into  heat.  We  say 
in  such  a  case  that  the  ray  has  been  absorbed.  If  a  ray 
of  light  passes  through  the  surface  of  the  transparent 
body,  normally,  its  direction  is  not  changed.  If,  however, 
it  meets  the  surface  at  an  oblique  angle,  it  will  be  bent 
from  its  path.  If  the  medium  into  which  the  light  thus 
passes  is  denser  than  that  from  which  it  comes,  as,  for 
example,  when  a  ray  passes  from  air  into  water,  or  glass 


378  THE  OUTLINES   OF  PHYSICS 

(Fig.  351),  it  will  be  bent  toward  the  normal  to  the  sur- 
face.    When  it  passes  through  a  surface  between  a  denser 


FIG.  351.  FIG.  352. 

and  a  rarer  medium,  as  when  the  ray  passes  from  glass 
into  air  (Fig.  352),  it  is  bent  away  from  the  normal  to  the 
surface.  A  ray  thus  bent  from  its  course  is  said  to  be 
refracted.  The  law  of  its  change  of  direction  follows 
a  fixed  law  ;  viz.  : 

343.  THE  LAW  OF  REFRACTION.  —  The  ratio  of  the 
sine  of  the  angle  of  incidence  to  the  sine  of  the  angle  of 
refraction  is  constant. 

The  law  may  be  expressed  thus, 


smr 

The  quantity  n  in  the  above  equation  is  called  the  index 
of  refraction. 

344.    EXPERIMENT    108.  —  Displacement    of    a    Ray    by  passing 
through  a  Sheet  of  Plate  Glass. 

Apparatus  : 

(1)  A  projecting  lantern,  or  porte  lumiere. 

(2)  A  piece  of  plate  glass. 

(3)  A  small  revolving  circular  stand. 
Procedure: 

(a)   In  front  of  the  condenser  set  up  a  diaphragm  containing  a 
vertical  slit,  and  focus  the  image  of  the  latter  upon  the  screen. 


REFLECTION  AND  REFRACTION 


379 


(5)    Mount  the   glass  vertically  upon  the  revolving  stand,  as  in 
Fig.  353,  securing  it  in  place  with  wax. 

Place  the  glass  in  front  of  the  objective  of  the  lantern  in  the  path 
of  the  ray,  and  turn  the  stand  upon  its  vertical  support. 

Note  the  displacement  of  the  image,  and  that 
when  the  light  traverses  the  glass  at  right  angles  the 
displacement  is  zero. 

If  the  experiment  were  performed  with  a  piece 
of  homogeneous  glass,  with  ab- 
solutely flat  and  parallel  sur- 
faces, it  would  be  possible  to 
show  from  the  relation  between 
the  angle  through  which  the 
glass  is  turned  and  the  dis- 
placement of  the  image,  that  a 
ray  of  light  in  passing  through 
a  refracting  medium,  the  faces 
of  which  are  parallel,  suffers 
lateral  displacement  but  no  per- 
manent change  of  direction.  In  other  words,  the  ray  is  bent  away 
from  the  normal  to  the  surface  (Fig.  354),  upon  emerging  from  the 
denser  medium,  just  as  strongly  as  it  had  been  bent  towards  it  upon 
entering  that  medium. 


i:tO 


Fro.  354. 


345.   The  Passage  of  Light  through  a  Prism.  — If,  in  the 

foregoing  experiment,  a  prism  of  glass  be  interposed  in 
the  path  of  the  ray  instead  of  the  plate  glass,  the  path  of 
the  ray,  after  traversing  the  prism, 
will  no  longer  be  parallel  to  its  orig- 
inal direction.  If  we  map  out  the 
path  of  the  ray  by  means  of  chalk 
dust,  as  described  in  Experiment  106, 
we  find  the  refracted  ray  bent  toward 
the  normal,  and  the  emerging  ray  bent  away  from  the 
normal,  as  in  the  case  of  the  plate  glass.  The  angle  at 
which  the  emerging  ray  meets  the  second  surface,  how- 


380 


THE  OUTLINES   OF  PHYSICS 


ever,  is  such  that  the  ray  acquires  a  new  direction.  (See 
Fig.  355.)  It  will  be  noted,  on  trying  the  experiment, 
that  the  image  is  broadly  fringed  with  color.  This  effect 
is  due  to  what  is  called  dispersion,  a  phenomenon  which 
will  be  fully  considered  in  Chapter  XL. 

346.  Total  Reflection.  —  When  a  ray  emerges  from  a 
denser  into  a  rarer  medium,  the  angle  r  (Fig.  356),  which 
the  emergent  ray  makes  with  the 
normal  to  the  surface,  is,  as  we  have 
seen,  always  greater  than  the  angle 
i  of  the  ray  in  the  denser  medium. 
If  the  angle  i  be  increased,  the 
emergent  ray  will  finally  take  a 
direction  parallel  to  the  surface. 
Any  further  increase  in  the  angle 
a  will  make  the  angle  greater  than 
FIG!  356.  90°.  The  ray,  therefore,  will  not 

emerge  at  all,  but  will  take  a  new 

path  within  the  denser  medium.  This  phenomenon  is 
called  total  reflection.  It  may  be  conveniently  studied  as 
follows : 


347.   EXPERIMENT  109.  —  Total  Reflection  in  Water. 

Apparatus  : 

(1)  A  large  beaker,  or  other  glass  vessel.     The  tanks  with  glass 
sides  used  for  aquariums  are  well  suited  to  this  experiment. 

(2)  A  projecting  lantern  or  porte  lumiere. 

(3)  A  plane  mirror. 

Procedure  : 

(a)  Cover  one  side  of  the  beaker,  or  tank,  with  black  paper,  leaving 
a  horizontal  slit  about  5  cm.  long,  and  1cm.  wide.  Fill  the  beaker 
with  water  in  which  a  few  drops  of  milk,  or  a  pinch  of  starch,  sufficient 
to  give  it  a  slightly  cloudy  appearance,  has  been  added.  Mount  the 


REFLECTION  AND  REFRACTION 


381 


beaker  upon  a  high  stand,  and  throw  a  beam  of  sunlight  obliquely 
upwards  upon  the  slit,  as  shown  in  Fig.  357. 

(6)  Observe  the  path  of  the  ray  within  the  liquid,  and  trace  out 
the  emerging  ray  in  the  air  above  by  means  of  chalk  dust.  Note 
carefully  also  the  existence  of  a  reflected  ray  within  the  liquid.  This 
ray  must  not  be  confused  with  that  produced  by  total  reflection.  It 


FIG.  357. 

is  a  case  of  ordinary  reflection  from  the  inner  surface  of  the  denser 
medium.  So  long  as  there  is  an  emergent  ray  in  the  air,  total  reflec- 
tion does  not  take  place. 

(c)  Increase  the  angle  which  the  ray  makes  with  the  surface  of  the 
water,  by  movement  of  the  mirror,  until  the  critical  angle  is  reached 
at  which  the  emergent  ray  becomes  parallel  to  the  surface.     Upon 
further  increasing  the  angle,  note  the  disappearance  of  the  refracted 
ray,  and  the  sudden  appearance  of  the  totally  reflected  ray  within  the 
liquid. 

(d)  To  the  observer  looking  at  the  surface  from  below  at  an  angle 
greater  than  the  critical  angle,  the  surface  appears  to  be  an  opaque 
mirror.     Objects  lying  in  the  air  beyond  are  entirely  hidden.     To 
verify  this  statement,  float  a  short  lighted  candle  upon  a  cork  on  the 
surface  of  the  liquid,    and  look   up  through  the  liquid  at  various 
angles. 


382  THE  OUTLINES   OF  PHYSICS 


CHAPTER   XL 

DISPERSION 

348.  The  Composition  of  White  Light.  —  It  has  already 
been  shown  that,  when  an  image  has  been  thrown  upon 
the  screen,  and  a  prism  is  interposed  in  the  path  of  the 
ray,  the  image,  which  is  displaced  from  its  position  by 
refraction,  exhibits  colors.  This  show  of  color  is  due  to 
the  fact  that  white  light  is  composed  of  various  rays  differ- 
ing in  wave  length.  Each  wave  length  has  its  distinctive 
color.  The  amount  of  refraction  which  a  ray  undergoes, 
however,  depends  upon  its  wave  length.  Short  waves  are 
more  bent  from  their  course  than  long  ones.  The  result  is 
that  the  violet  rays,  which  have  the  shortest  wave  lengths, 
are  most  displaced  by  the  action  of  the  prism,  while  the 
red  wave  lengths,  which  are  longest,  are  least  displaced. 
This  phenomenon  of  varying  refraction  according  to  the 
wave  of  length  is  called  dispersion.  When  a  beam  of  white 
light  passes  through  a  prism,  each  of  the  countless  wave 
lengths  of  which  it  is  made  up  is  displaced,  and  forms  a 
colored  image  upon  the  screen.  These  images  overlap, 
but  they  do  not  coincide.  In  the  center  of  the  composite 
image  thus  formed,  the  rays  from  the  overlapping  images 
recombine  to  give  the  appearance  of  white ;  at  the  ends, 
however,  red  shading  into  yellow,  and  violet  into  blue, 
respectively,  show  themselves.  If,  in  place  of  the  circular 
aperture,  a  vertical  slit  be  used,  these  colored  images  will 
be  reduced  almost  to  a  line.  They  will  then  overlap 
scarcely  at  all,  and  each  color  will  stand  out  unmixed. 


DISPERSION  383 

349.  The   Spectrum.  —  The   number   of   different   wave 
lengths  which  are  present  in  a  beam  of  white   light  is 
very  great,  perhaps  infinite ;   consequently,  when  we  dis- 
perse such  light  by  means  of  a  prism,  we  do  not  find  a 
series  of  colored  images  separated  from  each  other  by  a 
dark  space,  but  a  continuous  series  merged  into  a  band  of 
gradually  changing  colors.     This  is  called  the  spectrum. 
Its  color  changes  by  insensible  gradations  from  red   to 
violet.     At  least  one  hundred  and  fifty  intervening  tints 
may  be   distinguished,  but   comparatively   few   of   these 
have  received  names.     Newton,  who  was  one  of  the  earli- 
est students  of  this  subject,  named  seven.     These,  in  the 
order  of  decreasing  wave  lengths,  are  :  red,  orange,  yellow, 
green,  blue,  indigo,  violet. 

350.  EXPERIMENT  110.  — The  Spectrum  is  made  up  of  a  Series  of 
Overlapping  Colored  Images. 

Apparatus  : 

(1)  A  lantern,  with  a  diaphragm,  containing  a  circular  opening. 

(2)  An  equiangular  prism  of  flint  glass. 

(3)  A  piece  of  ruby  glass.1 
Procedure  : 

(a)  Set  up  the  diaphragm  in  front  of  the  lantern  with  the  beam  of 
light,  making  an  angle  of  about  70°  with  the  wall.  Adjust  the  lens 
so  that  an  image  will  be  formed  upon  a  screen  at  a  distance  equal  to 
that  of  the  lens  from  the  wall.  (See  Fig.  358.)  In  front  of  the  lens, 
mount  the  prism,  as  shown  in  the  figure.  The  rays  falling  upon  the 
prism  will  be  refracted  and  dispersed,  and  will  form  a  very  impure 
spectrum  upon  the  screen. 

(6)  Hold  the  piece  of  ruby  glass  between  the  diaphragm  and  lens, 
or,  indeed,  anywhere  in  the  path  of  the  ray,  and  note  the  effect  upon 

1  Ruby  glass  is  a  variety  of  red  glass  selected  for  use  in  photography 
because  it  transmits  only  red  light,  with  a  small  amount  of  orange  and  a 
trace  of  yellow.  These  are  the  colors  to  which  the  plates  used  in  pho- 
tography are  least  sensitive. 


384  THE  OUTLINES   OF  PHYSICS 

the  spectrum.  It  will  be  seen  that,  owing  to  the  opacity  of  the  glass 
to  all  rays  except  the  red  and  orange,  the  spectrum  is  reduced  to  a 
red  and  nearly  circular  image  of  the  aperture.  This  image,  which  is 
somewhat  elongated  horizontally,  is  not  of  one  color  throughout.  On 
one  side  it  is  of  a  deep  red,  and  on  the  other  it  is  orange  or  yellow. 
Ruby  glass  really  transmits  more  than  one  wave  length  of  light,  and 
the  image  consists  of  the  overlapping  series  of  images  which  go  to 
form  the  red  and  orange  ends  of  the  spectrum.  If  we  could  take 
away  all  of  these  images  but  one,  we  should  find  the  spectrum  reduced 
to  an  image  of  the  aperture  uniform  in  color  and  of  the  same  appear- 
ance as  though  the  light  had  not  been  passed  through  the  prism. 


CONDENSER       DIAPHRAGM 


FIG.  358. 

(c)  In  order  to  produce  a  spectrum  which  contains  but  one  color, 
we  must  use  as  a  source  of  light  some  incandescent  vapor.  The  most 
convenient  vapor  for  this  purpose  is  that  of  sodium.  Remove  the 
lamp  from  the  lantern  and  put  in  its  place  a  Bunsen  burner.  Intro- 
duce into  the  flame,  by  means  of  a  pair  of  tweezers  improvised  from 
iron  wire,  a  small  piece  of  metallic  sodium.  The  yellow  flame  which 
results  from  the  burning  of  this  metal  contains  light  of  one  wave 
length  only  (monochromatic  light).  The  spectrum  formed  upon  the 
screen  will,  therefore,  be  reduced  to  a  single  yellow  image  of  the 
aperture  in  the  diaphragm.  Were  the  sodium  flame  reduced  almost 
to  a  point  like  the  arc  light  or  a  lime  light,  this  image  would  be  well 
denned  and  circular  in  form.  Owing  to  the  great  size  of  the  flame, 
the  image  is  not  very  distinct  in  its  outlines. 

351.    EXPERIMENT  111.  — The  Formation  of  a  Pure  Spectrum. 

Apparatus  : 

(1)  In  order  to  reduce  the  width  of  the  overlapping  images  which 
form  the  spectrum,  and  thus  to  prevent  them  from  mixing,  it  is  neces- 


EC 


.-I 


DISPERSION  385 

sary,  as  has  already  been  pointed  out,  to  use  a  slit  in  place  of  the 
circular  aperture  of  the  last  experiment.  A  slit  suitable  for  use  in  the 
present  experiment  may  be  constructed  as  follows  : 

Take  two  wooden  blocks  10  cm.  x  10  cm.  x  5  cm.  each.  Bevel 
the  end  of  one,  as  shown  in  Fig.  359.  The  edges  which  are  in  contact, 
when  placed  as  shown  in  the  figure,  should 
match  perfectly.  Lay  the  blocks  together,  as 
above,  upon  a  flat  surface,  and  attach  a  pair  of 
brass  hinges  as  shown.  When  the  beveled 
block  swings  upon  these  hinges,  the  matched 
edges  will  move  apart,  forming  an  opening 
with  parallel  sides  (a  slit).  A  spring  clip 
screwed  to  the  square  block  and  rubbing 
against  the  surface  of  the  beveled  block 

TTm     ^^Q 

will  suffice  to  hold  the  arrangement  in  any 

desired  position.  Screw  the  square  block  to  the  face  of  a  larger 
block  (20  cm.  square)  so  that  the  slit  will  bisect  a  round  hole,  2  cm. 
in  diameter,  in  the  center  of  the  latter. 

(2)  The  lantern,  lens,  and  prism  described  in  the  foregoing  ex- 
periment. 

Procedure  : 

(a)  Open  the  slit  to  a  considerable  width  (about  1  cm.).  Adjust 
the  apparatus  so  as  to  give  a  well-defined  spectrum.  The  prism  should 
be  turned  into  such  a  position  that  the  deviation  of  the  ray  from  its 
course  is  as  small  as  possible.  This  is  called  the  position  of  minimum 
deviation. 

(6)  Close  the  slit  gradually  and  note  the  effect  upon  the  appear- 
ance of  the  spectrum.  It  will  be  seen  that  while  the  brightness 
diminishes,  the  intensity  of  color  throughout  deepens.  The  central 
portions  of  the  spectrum,  which  were  greatly  mixed  by  the  overlap- 
ping of  the  broad  images,  now  begin  to  show  the  rich  colors  of  the 
pure  spectrum.  These  changes  continue  until  the  slit,  the  edges  of 
which  are  necessarily  imperfect,  come  into  contact  at  certain  points. 
These  points  bar  the  passage  of  the  light  and  produce  dark,  horizontal 
striations  through  the  spectrum.  The  more  perfectly  straight  and 
smooth  the  edges  of  the  slit  and  the  more  nearly  parallel  its  two  jaws, 
the  narrower  it  can  be  made  without  introducing  these  striations. 

(c)  Repeat  the  above  operation,  using  a  sodium  light  in  place  of 
the  light  of  the  lantern.     Note  that  the  yellow  image  to  which  the 
2c 


386  THE  OUTLINES   OF  PHYSICS 

spectrum  is  reduced  grows  narrower  as  the  slit  is  diminished  in  width, 
until  it  becomes  a  mere  vertical  yellow  line. 

352.  Classes  of  Spectra.  —  Spectra  are  usually  classified 
as  follows : 

(1)  Continuous  spectra.     (The  spectra  of  glowing  solids 
or  liquids.) 

(2)  Bright-line  spectra.     (The  spectra  of  glowing  gases 
or  vapors.) 

(3)  Absorption  spectra.     (Spectra  produced  by  the  dis- 
persion of  light  which  has  passed  through  some  medium 
capable  of  absorbing  certain  wave  lengths  and  transmitting 
others.) 

In  the  foregoing  experiments  we  have  seen  examples  of 
continuous  spectra,  of  the  simplest  sort  of  an  absorption 
spectrum  (when  ruby  glass  was  interposed  and  the  entire 
spectrum  was  cut  off,  excepting  the  rays  at  the  red  end). 
Also  the  simplest  possible  form  of  a  bright-line  spectrum 
(that  of  sodium  vapor). 

353.  Dark-line   Spectra. — It  is  a  universal  property  of 
matter  that  all   substances  absorb   precisely  those  kinds 
of  light  which  they  are  capable    of   emitting  when  ren- 
dered incandescent,  and   no    others.      It   follows,    there- 
fore, that  gases,  the  spectra  of  which  consist  of  bright 
lines,  will  absorb  light  only  of   the  wave  lengths  which 
they  emit,  and  will  produce  spectra  with  black  lines  cor- 
responding  in   position  with    the  bright  lines  which  the 
gas  in  question  radiates.     This  principle,  which  is  of  the 
utmost  importance  in  the  science  of  spectroscopy,  may  be 
demonstrated 'as  follows: 

354.  EXPERIMENT  112.  — Reversal  of  the  Sodium  Line. 

Apparatus : 

(1)  The  lantern  with  slit,  lens,  and  prism. 

(2)  A  sodium  flame. 


DISPERSION  387 

Procedure : 

(a)  Mount  the  apparatus  so  as  to  produce  a  fairly  pure  spectrum 
upon  the  screen. 

(6)  In  the  path  of  the  ray,  between  the  slit  and  lens,  introduce  a 
large  sodium  flame.  This  may  be  conveniently  produced  as  follows  : 

Take  a  piece  of  asbestos  wicking  or,  if  this  cannot  be  obtained, 
some  loosely  woven  cotton  or  hemp  yarn.  Roll  into  a  loosely  wound 
ball  at  the  end  of  a  wire  holder ;  dip  the  ball  into  alcohol  and  lay  upon 
it  two  or  three  small  bits  of  metallic  sodium.  Mount  the  wicking  just 
below  the  path  of  the  ray,  midway  between  the  lens  and  slit,  and  ignite. 
The  result  will  be  a  large  flame  with  the  characteristic  yellow  color 
of  burning  sodium.  The  rays  passing  through  this  mass  of  sodium 
vapor,  which  is  opaque  to  the  yellow  light,  will  suffer  absorption.  Note 
that  the  spectrum  is  otherwise  continuous  and  possesses  a  black  line  in 
the  region  corresponding  to  that  where  the  bright  line  of  sodium  in  the 
previous  experiment  appeared.  The  identity  in  the  position  of  this 
black  line  and  the  bright  line  of  sodium  may  be  shown  by  removing 
the  sodium  flame  from  between  the  lens  and  the  slit  and  introducing 
one  in  the  place  of  the  light  within  the  lantern,  as  described  in  Ex- 
periment 109. 

355.  The  Fraunhofer  Lines.  —  When,  in  1819,  the  sun's 
spectrum  was  observed,  using  a  narrow  slit  instead  of  the 
wide  apertures  which  had  been  employed  by  Newton  and 
other  earlier  students  of  this  subject,  it  was  found  that  the 


FIG.  360. 


sun's  spectrum  was  filled  with  black  lines  instead  of  being, 
as  had  been  previously  supposed,  continuous.  The  first 
to  notice  these  lines  and  to  describe  them  was  a  German 
physicist  by  the  name  of  Fraunhofer,  and  they  are  still 


388  THE  OUTLINES  OF  PHYSICS 

known  by  his  name.  He  observed  the  presence  of  many 
hundreds  of  these  lines,  and  designated  the  most  promi- 
nent of  them  by  the  letters  A,  B,  (7,  D,  E,  F,  a,  and  H. 
The  location  of  these  lettered  lines  is  shown  in  Fig.  360. 
Many  years  later  it  was  shown  by  Kirchhoff  and  Bunsen 
that  the  bright  line  of  sodium,  the  position  of  which  cor- 
responded exactly  with  the  black  line  D  of  Fraunhofer, 
was  capable  of  reversal,  that  is  to  say,  of  being  changed 
into  a  black  line  by  the  interposition  of  sodium  vapor. 
Experiment  112  is  a  reproduction  in  the  simplest  form  of 
their  experiment.  They  concluded  that  the  lines  of  Fraun- 
hofer, and  the  innumerable  other  black  lines  of  the  solar 
spectrum,  were  produced  by  the  passage  of  the  light  of  the 
sun  through  incandescent  vapors  in  the  sun's  atmosphere ; 
and  they  showed  in  support  of  their  view  that  hundreds 
of  bright  lines,  which  constitute  the  bright-line  spectrum 
of  iron,  correspond  exactly  in  position  to  dark  lines  in  the 
solar  spectrum,  and  that  other  of  these  dark  lines  have 
their  counterparts  in  the  bright  lines  due  to  glow- 
ing vapors  of  various  materials  found  in  the  earth's 
crust. 


356.   EXPERIMENT  113.  —  The  Absorption  Spectra  of  Chlorophyl 
and  of  Potassium  Permanganate. 

Apparatus  : 

(1)  The  lantern  with  slit,  lens,  and  prism  as  previously  described. 

(2)  About  200  c.c.  of  chlorophyl  solution.     This  is  readily  pre- 
pared by  placing  a  handful  of  green  clover  leaves  or  of  fresh  grass 
in  alcohol.     Warm  slightly,  bruise  the  leaves  by  stirring,  and  shake 
well  for  several  minutes,  then  pour  off  the  liquid,  which  will  be  of 
a  rich  green  color.      This  solution,  if  bottled,  will  hold  its  color 
for  a  considerable  time. 

(3)  A  solution  of  potassium  permanganate  made  by  dissolving 
a  few  crystals  of  that  substance  in  water. 


DISPERSION 


389 


Procedure : 

(a)  Having  adjusted  the  apparatus  so  as  to  project  a  well-defined 
spectrum  upon  the  screen,  interpose  a  flat  glass  cell  containing  the 
chlorophyl  solution  in  the  path  of  the  ray.  Note  the  formation 
of  dark  bands  produced  by  the  absorption  of  the  colors  corresponding 
to  those  regions  of  the  spectrum  which  are  absorbed  in  passing 
through  the  solution.  One  of  these  bands  lies  in  the  red,  two  in 
the  yellow  and  green.  The  extreme  Ted  end  of  the  spectrum  like- 
wise suffers  absorption,  as  does  to  some  extent  the  entire  blue  end. 


FIG.  361. 

(&)  Substitute  for  the  chlorophyl  a  very  dilute  solution  of  the 
potassium  permanganate,  and  note  that  an  entirely  different  set  of 
bands  are  produced.  Strengthen  the  solution  from  time  to  time,  and 
note  the  increased  blackness  of  the  bands  as  the  absorption  becomes 
more  marked ;  also  the  reappearance  of  new  ones.  Note  the  distinc- 
tion between  the  absorption  bands  produced  by  the  passage  of  light 
through  a  liquid  and  the  black  lines  which  are  obtained  when  a 
vapor  is  interposed  in  the  path  of  the  ray.  Figure  361  shows  the 
characteristic  absorption  spectrum  of  chlorophyl. 


390 


THE  OUTLINES   OF  PHYSICS 


CHAPTER   XLI 

LENSES 

357.  Lenses  defined.  —  A  piece  of  glass  or  other  trans- 
parent material,  the  surfaces  of  which  are  curved  in  such 
a  manner  that  a  beam  of  transmitted  light  is  brought 
to  a  focus  in  consequence  of  refraction,  is  called  a  lens. 
The  only  types  of  lenses  which  it  will  be  necessary  to 

/i 


L 


FIG.  362. 

consider  here  are  those  in  which  the  faces  are  portions 
of  a  spherical  surface  (spherical  lenses).  Sometimes  the 
radius  of  curvature  of  one  face  of  a  lens  is  infinite,  in 

which  case  that  face  is  a 
plane.  Sometimes  the  cen- 
ter of  curvature  is  on  one 
side  and  sometimes  on  the 
other,  giving,  respectively, 
convex  and  concave  faces. 
All  spherical  lenses  belong  to 
one  of  the  six  forms  shown 
in  Fig.  362.  Of  these  the  first  three  are  thicker  in  the 
middle  than  at  the  edges.  All  such  lenses  bring  the  ray 
to  a  focus  beyond  the  lens,  as  shown  in  Fig.  363.  The 


FIG.  363. 


LENSES 


391 


other  three  forms  are  thinner  in  the  middle  than  at  the 
edges.  Such  lenses  cause  parallel  rays  to  diverge.  (See 
Fig.  364.)  The  focus  of  such  a  lens  lies  in  an  imaginary 


FIG.  364. 

point  on  the  side  of  the  lens  from  which  the  rays  have 
come.  The  first  class  is  called  converging,  the  second 
diverging  lenses. 

358.  Formation  of  Images  by  Means  of  Lenses.  —  If  we 

have  a  source  of  light  at  a  point  /  on  one  side  of  a  con- 
verging lens,  rays  reaching  the  lens  from  this  point  will 
be  refracted,  and  will  come  to  a  focus  at  a  point  f  on 
the  other  side.  In  the  same  mariner  a  source  of  light 
at  f  will  have  its  rays  brought  to  a  focus  at  /.  The 
points  f  and  fr  are  called  conjugate  foci  of  the  lens. 

If  the  point  /  be  moved  to  an  infinite  distance  so  that 
the  rays  from  it  are  parallel,/'  will  approach  the  lens,  reach- 
ing finally  a  point  F'.  This  is  called  the  principal  focus 
of  the  lens.  If,  in  the  same  way,  a  source  of  light  at  /'  be 
moved  off  to  an  infinite  distance,  its  rays  will  come  to  a 
focus  at  F  (Fig.  365).  The  distance  from  the  lens  to  the 
principal  focus  is  called  the  focal  length  of  the  lens.  The 
position  of  /  and  /'  is  defined  by  means  of  the  equation 


u 


392 


THE  OUTLINES  OF  PHYSICS 


in  which  u  and  v  are  the  distances  of  /  and  /'  from  the 
lens  and  L  is  the  focal  length.     If  instead  of  a  single 


FIG.  365. 


point  we  have  an  object  on  one  side  of  the  lens,  as  in 
Fig.  366,  light  from  all  points  of  the  object  will  be  brought 
to  a  focus  at  the  corresponding  point  behind  the  lens,  and 
the  result  will  be  an  image.  This  image,  like  the  image 


FIG.  366. 

formed  by  a  concave  mirror,  will  be  inverted.  Its  size  and 
its  distance  from  the  lens  will  depend  upon  the  size  and 
distance  of  the  object  in  accordance  with  the  principles 
stated  above.  If  the  object  be  brought  nearer  the  lens 
than  the  principal  focus  F,  its  image  will  vanish  at  infinity 
on  the  other  side.  The  rays  after  refraction  now  become 


LENSES 


393 


divergent  instead  of  convergent.     Their  only  focus  is  on 
the  other  side  of  the  lens,  and  is  imaginary.     The  image 


ceases  to  be  real  and  becomes  virtual.     It  is  erect  and  on 


FIG.  367. 

the  same  side  of  the  lens  as  the  object.  (See  Fig.  367.) 
Diverging  lenses  are  capable  of  forming  only  virtual 
images. 

359.  The  Telescope.  —  This  is  one  of  the  most  important 
of  optical  instruments.  In  the  case  of  the  telescope  a 
real  image  of  a  distant  object  is  produced  by  means  of 
a  lens  or  a  concave  mirror.  This  real  image,  which 


FIG.  368. 


is  necessarily  much  smaller  than  the  object,  but  near  at 
hand,  is  magnified  by  means  of  another  lens  or  combi- 
nation of  lenses  called  the  eyepiece.  Figure  368  shows 
the  simplest  possible  arrangement  of  a  telescope.  The  lens 
0,  by  means  of  which  the  real  image  is  formed,  is  called 


394  THE  OUTLINES  OF  PHYSICS 

the  object  lens,  or  the  objective.  The  method  of  magni- 
fying the  real  image  at  the  eyepiece  consists  in  bringing 
a  small  lens  so  near  to  the  image  as  to  produce  a  virtual 
image  of  it.  As  a  rule,  a  combination  of  two  lenses  is 
used  both  in  the  objective  and  eyepiece  instead  of  one; 
but  the  object  of  the  lenses,  whatever  the  construction 
may  be,  is  that  stated  above. 

The  size  of  the  image  produced  by  a  lens  is  proportional-, 
first,  to  the  size  of  the  object,  and,  secondly,  to  the  focal 
length  of  the  lens.  It  is  independent  of  the  aperture 
of  the  lens.  The  brightness  of  the  image,  which  is  a 
matter  of  great  importance  in  telescopes  used  in  astron- 
omy, where  the  objects  to  be  studied  are  very  dim,  is 
directly  proportional  to  the  aperture  of  the  lens.  The 
statement  that  the  size  of  the  image  is  independent  of 
the  aperture  of  the  lens  may  be  verified  by  means  of  the 
following  experiment: 

360.  EXPERIMENT  114.  — Measurement  of  the  Image  formed  by  a 
Lens  of  Varying  Aperture. 

Apparatus : 

(1)  A  converging  lens ;  the  longer  the  focus  and  the  greater  the 
diameter  of  this  lens,  the  better. 

(2)  A  candle ;  a  screen. 

(3)  A  sheet  of  paper. 

Procedure : 

(a)  Mount  the  lens  as  shown  in  Fig.  369,  so  as  to  throw  an  inverted 
image  of  the  lighted  candle  upon  the  screen. 

(&)  Measure  the  diameter  of  the  candle  itself  just  below  the  wick, 
and  the  diameter  of  the  corresponding  portion  of  the  image.  The 
ratio  of  this  diameter  gives  the  magnifying  power  of  the  arrangement. 
The  image  may  be  larger  or  smaller  than  the  object,  according  to  their 
relative  distances  from  the  lens. 

(c)  Cut  a  hole  in  the  piece  of  paper  as  nearly  circular  as  convenient, 
and  about  0-5  cm.  in  diameter.  Insert  the  paper  just  behind  the  lens 


LENSES 


395 


until  the  hole  corresponds  with  the  center  of  the  latter ;  the  aperture 
of  the  lens  is  now  reduced  to  the  size  of  the  hole.  Fasten  the  paper 
in  this  position  and  note,  first,  that  the  image  of  the  candle  is  still 


FIG.  369. 


present ;  second,  that  it  is  much  less  brilliant  than  before.  Measure 
the  diameter  of  the  candle  as  in  operation  (&).  It  will  be  found  that 
the  image  is  of  the  same  size  as  when  the  entire  aperture  of  the  lens 
was  utilized. 

361.   EXPERIMENT  115.  —  Relation  between  the  Size  of  the  Image 
and  the  Focal  Length  of  the  Lens. 
Apparatus : 

(1)  Two  converging  lenses  which  differ  considerably  in  focal  length. 

(2)  A  candle. 

(3)  Two  small  cardboard  screens. 
Procedure : 

(a)  Mount  the  lenses  2  m.  apart,  as  shown  in  Fig.  370,  with  the 
lighted  candle  midway  between  them.    Shift  the  two  cardboard  screens 


396  THE  OUTLINES   OF  PHYSICS 

back  and  forth  behind  the  lenses,  until  the  images  of  the  candle  are  in 
focus  upon  them.  Measure  the  diameter  of  the  candle  in  each  image, 
and  also  the  distance  from  the  lens  to  the  screen.  It  will  be  found 
that  these  diameters  are  proportional  to  the  respective  distances. 


A 


FIG.  370. 

362,  Magnifying  Power  of  a  Telescope.  —  The  magnifying 
power  of  a  telescope  depends  not  only  upon  the  size  of 
the  real  image  formed,  but  upon  the  size  of  the  virtual 
image  obtained  by  the  use  of  the  eyepiece.     Magnifying 
power  is  expressed  in  terms  of  the  size  of  this  virtual  image 
as  it  appears  to  the  eye,  compared  with  the  size  of  the 
object  itself,  when  viewed  without  the  aid  of  the  telescope. 
It  is  sometimes  possible  to  make  this  comparison  directly, 
as  in  the  example  afforded  by  the  following  experiment : 

363.  EXPERIMENT  116.  —  The  Measurement  of  Magnifying  Power. 

Apparatus : 

A  spyglass  or  reading  telescope  similar  to  that  used  with  the  gal- 
vanometer. (See  Appendix  VIII.) 

Procedure : 

(a)  Set  up  the  telescope  at  a  distance  of  several  meters  from  a 
vertical  scale  (a  white  board  divided  to  decimeters  is  useful  for  this 
purpose),  and  get  the  latter  carefully  in  focus.  Close  the  left  eye  and 
get  the  right  eye  well  fixed  upon  the  image  of  the  scale  in  the  eye- 
piece ;  then  open  the  left  eye  and  look  with  it  at  the  scale  itself.  It 
will  be  found  possible  with  a  little  practice  to  see  the  image  and  the 
scale  simultaneously,  and  with  a  slight  movement  of  the  eyes  to  bring 
these  side  by  side. 

(&)  Having  acquired  the  power  of  seeing  with  the  two  eyes  inde- 
pendently as  above,  note  the  number  of  scale  divisions  which  the 


LENSES  397 

image  of  one  scale  division,  as  viewed  in  the  telescope,  corresponds 
to.  This  number  gives  directly  the  magnifying  power  of  the  instru- 
ment. If  several  eyepieces  differing  in  magnifying  power  are  avail- 
able, —  and  it  is  often  possible  to  adapt  the  eyepieces  of  microscopes 
to  this  purpose,  —  measurements  may  be  made  with  each. 

When  it  is  desired  to  determine  roughly  the  magnifying  power  of 
a  spyglass  or  field  glass  of  any  kind,  there  are  many  familiar  objects 
out  of  doors  which  may  be  made  to  serve  as  a  scale.  The  tiers  of 
brick  in  the  wall  of  a  house  or  chimney,  for  example,  afford  a  very 
good  scale  of  comparison,  provided  the  distance  is  not  so  great  as  to 
make  them  undistinguishable  to  the  naked  eye.  The  equidistant 
pickets  of  a  fence  may  often  be  made  to  serve  as  a  horizontal  scale 
for  such  a  purpose. 

364.  Spherical  Aberration.  —  We  may  regard  a  lens  as 
made  up  of  a  great  number  of  elements  or  parts,  each  one 
of  which  is  capable  by  itself  of  forming  a  complete  image. 
If,  for  example,  in  Experiment  114  the  sheet  of  paper  with 
the  small  aperture  had  been  moved  around  so  as  to  admit 
light  from  different  portions  of  the  lens  successively,  the 
image  would  continue  to  exist  whatever  the  position  of 
the  aperture  might  be.  The  image  obtained  by  the  use 
of  the  whole  lens  is  formed  by  the  overlapping  of  these 
images.  The  images  formed  by  different  portions  of  a 
spherical  lens  do  not,  however,  coincide  accurately  in 
position.  There  is  therefore  a  blurring  of  the  resultant 
image.  This  is  due  to  what  is  called  spherical  aberra- 
tion. The  fact  that  the  images  formed  by  the  various 
parts  of  the  lens  do  not  perfectly  coincide  may  be  shown 
by  the  method  just  indicated ;  namely,  by  mounting  a  dia- 
phragm with  a  small  aperture  close  to  the  lens,  and  then 
moving  it  around.  It  will  be  seen  that  the  image  shifts 
its  position  slightly  as  the  aperture  moves  across  the  lens 
from  side  to  side. 

A  lens  with  spherical  surfaces,  in  point  of  fact,  brings 


398 


THE  OUTLINES   OF  PHYSICS 


a  beam  of  light  which  passes  through  it  near  the  edge,  to 
a  focus  (CL)  at  a  point  slightly  nearer  the  lens  than  the 
focus  (&)  of  the  beam  which  passes  through  its  center. 
(See  Fig.  371.) 


a    b 


FIG.  371. 


Spherical  aberration  is  reduced  by  using  parabolic  in- 
stead of  spherical  surfaces,  and  by  the  use  of  a  diaphragm 
or  stop  which  reduces  the  aperture  of  the  lens  to  as  small 
an  area  as  the  dimness  of  the  image  will  allow. 

365.  Chromatic  Aberration.  —  Another  error  of  lenses  is 
due  to  the  fact  that  different  colors  are  differently  re- 
fracted. On  account  of  dispersion  of  light  within  the  lens, 
violet,  which  is  the  most  strongly  refracted,  comes  to  a 
focus  at  a  point  nearer  the  lens  than  do  the  other  colors ; 
and  red,  which  has  the  longest  wave  length,  comes  to  a 
focus  at  the  greatest  distance.  Between  these  two  are  the 
foci  of  all  intermediate  colors.  The  consequence  is  that  a 
series  of  colored  images  are  formed  one  behind  the  other. 
For  the  most  part  these  colored  images  overlap,  and  their 
colors  mingle  and  neutralize  each  other.  Around  the  edge 
of  the  beam  of  light  from  a  lens,  however,  there  is  always 
a  fringe  of  color.  This  can  be  observed  by  closely  examin- 
ing the  image  of  a  candle  formed  by  one  of  the  lenses  used 
in  the  foregoing  experiments.  The  fact  that  violet  comes 
to  a  focus  nearest  the  lens,  and  red  farthest  away,  can  be 
demonstrated  by  the  following  experiment : 


LENSES 


399 


366.  EXPERIMENT  117.  —  Chromatic  Aberration  of  a  Lens. 

Apparatus  : 

(1)  A  lantern. 

(2)  A  diaphragm  with  a  round  hole,  to  be  used  in  front  of  the 
condenser. 

(3)  A  simple  converging  lens. 

Procedure  : 

(a)  Remove  the  objective  of  the  lantern  and  set  up  the  ordinary 
lens  in  its  place,  so  as  to  bring  the  opening  in  the  diaphragm  to  a 
focus  at  a  distance  of  2  or  3  m.  in  front  of  the  lantern. 

(b)  Take  one  of  the  cardboard  screens  used  in  Experiment  115,  and 
move  it  along  the  path  of  the  ray  beyond  the  lens.    It  will  be  seen 
that  the  cone  of  light  lying  between  the  lens  and  the  focus  is  sur- 
rounded by  a  ruddy  fringe  or  border.     This  is  due  to  the  fact  that 
red  light  is  not  so  greatly  bent  from  its  course  as  are  the  other  colors. 

(c)  Move  the  screen  away  from  the  lens  until  it  passes  through 
the  focus  and  intercepts  the  diverging  cone  beyond  that  point.     It 
will  now  be  foluid  that  the  red  fringe  has  been  supplanted  by  a  bluish 
one. 

367.  Achromatic  Lenses. — Achromatic  aberration  in  lenses 
is  corrected  by  making  use  of  a  combination  of  two  lenses 
differing  greatly  in  dispersive  power.     If  we  take  a  bicon- 


FIG.  372. 


vex  lens  ((7,  Fig.  372)  of  crown  glass,  the  dispersive  power 
of  which  is  slight,  the  violet  light  will  be  brought  to  a 
focus  at  v  and  red  light  at  r.  By  placing  behind  this  a 
diverging  lens  of  flint  glass  (F,  Fig.  373),  which  is  much 
more  highly  dispersive,  the  violet  rays,  which  tend  to  a 


• 


400 


THE  OUTLINES  OF  PHYSICS 


CROWN 


focus  too  soon,  will  be  bent  outward  more  strongly  than 
will  the  red,  and  it  is  possible  to  construct  these  lenses  so 
that  both  sets  of  rays  will  come  to  a  common  focus  at 

vr  (Fig.  374).  Such  a  com- 
bination is  called  an  achro- 
matic lens.  Achromatic 
lenses  are  always  used  in 
the  objectives  of  telescopes, 
microscopes,  and  other  opti- 
cal instruments  where  chro- 
matic aberration  would  be 
detrimental. 

368.  The     Microscope.  — 

The  essential  parts  of  this 
instrument,  namely,  the  ob- 
jective and  the  eyepiece,  are  the  same  as  in  the  tele- 
scope; but  the  objective  is  modified  to  adapt  it  to  the 
work  for  which  the  microscope  is  intended.  This  consists 
in  producing  an  enlargg-d  real  image  of  a  small  object 
near  at  hand,  and  further  magnifying  this  image  by 


FIG.  373. 


FIG.  374. 


means  of  the  eyepiece.  The  objective  is  therefore  a  very 
small,  short-focused  combination  of  lenses  so  constructed 
as  to  be  achromatic.  When  this  is  brought  near  the  object 
to  be  observed,  a  real  image  is  formed  in  the  eyepiece,  the 
diameter  of  which  is  great,  as  compared  with  that  of  the 


LENSES  401 

object,  in  proportion  to  its  distance  from  the  lens.  A 
virtual  image  of  this  is  formed  by  means  of  an  eyepiece", 
as  has  already  been  explained  in  the  case  of  the  telescope. 
In  Fig.  375,  the  essential  parts  of  a  microscope  are  shown. 


FIG.  375. 

For  simplicity,  the  objective  and  eyepiece  are  represented 
as  simple  lenses.1 

As  in  the  former  case,  the  magnifying  power  is  expressed 
by  means  of  the  increased  apparent  diameter  of  the  virtual 
image,  not  in  terms  of  its  area.  The  magnifying  powers 
of  microscopes  sometimes  exceed  one  thousand  diameters. 

In  physics,  the  microscope  is  chiefly  used  for  purposes 
of  measurement.  Three  different  methods  are  employed: 

(1)  The  stage  upon  which  the  object  under  observation 
is  mounted  is  moved  along  under  the  objective  by  means 
of  a  micrometer  screw. 

(2)  The  cross-hair  of  the  eyepiece  is  moved  through  the 
field  of  view  by  means  of  a  micrometer  screw. 

(3)  A  glass  scale,  divided  to  tenths  of  a  millimeter,  is 
placed  in  the  focus  of  the  eyepiece  so  that  the  image  of 
objects  under  observation  will  be  superimposed  upon  it. 
In  order  to  reduce   these  readings  to  centimeters,  it  is 
necessary  to  place  under  the  objective  another  scale  ruled 

1  For  further  information  concerning  the  microscope,  see  Appendix  IV ; 
also  Gage's  Microscopical  Methods. 

2D 


402  THE  OUTLINES   OF  PHYSICS 

to  such  fine  divisions  that  the  whole  of  at  least  one  divi- 
sion will  come  within  the  field.  The  size  of  the  image  of 
this  division  upon  the  eyepiece  micrometer  having  been 
noted,  the  value  of  a  scale  division  of  the  eyepiece  microm- 
eter can  be  computed.  This,  which  is  the  simplest  method 
of  micrometric  measurement,  can  be  illustrated  by  means 
of  the  following  experiment  (see  Appendix  IV)  : 

369.   EXPERIMENT  118.  —  Measurement  of  the  Diameter  of  a  Hair. 

Apparatus : 

(1)  A  microscope  with  a  low-power  objective  (1  or  2  cm.),  and 
an  eyepiece  provided  with  a  glass  micrometer. 

(2)  A  scale  ruled  upon  glass,  the  divisions  of  which  do  not  exceed 
tenths  of  millimeters. 

Procedure : 

(a)  Place  the  glass  ruling  upon  the  stage,  and  focus  the  microscope 
upon  it.  Determine  the  value  of  one  division  of  the  eyepiece  microm- 
eter in  terms  of  the  glass  ruling,  the  value  of  which  must  be  known, 

•  (&)  Lay  the  hair  upon  the  stage,  holding  it  taut  by  means  of  wax, 
and  adjust  so  that  it  will  lie  parallel  to  the  lines  of  the  eyepiece 
micrometer.  Kead  its  diameter  upon  the  scale  of  the  latter,  and 
reduce  those  readings  to  centimeters  by  means  of  the  foregoing  deter- 
mination of  the  value  of  the  scale  division  of  the  micrometer.  The 
diameter  of  small  wires,  and  of  any  objects  minute  enough  to  come 
entirely  within  the  field  of  the  microscope,  can  be  measured  in  this 
way. 

(For  a  full  discussion  of  the  systems  of  lenses  used  in  various  opti- 
cal instruments,  see  Elements  of  Physics,  Vol.  Ill,  Chaps.  I  to  VI.) 


POLARIZATION  AND  DOUBLE  REFRACTION       403 


CHAPTER  XLII 

« 

POLARIZATION,   DOUBLE  REFRACTION  AND  INTERFERENCE 

370.  Polarization  by  Reflection.  —  We  may  consider  a 
ray  of  ordinary  light,  which  may  be  said  to  contain  vibra- 
tions in  every  possible  plane,  to  be  made  up  of  two  com- 
ponent vibrations  at  right  angles  to  each  other.  Imagine 
a  plane  mirror  placed  obliquely  to  this  ray,  and  that  one 
of  the  components  of  the  ray  vibrates  in  a  direction  par- 
allel to  the  surface  of  the  mirror,  while  the  other  makes  an 
angle  with  the  same.  It  is  natural  to  suppose  that  these 
two  components  would  be  affected  differently  upon  reach- 
ing the  surface.  In  point  of  fact, 
it  is  found  that  one  of  them  tends 
to  penetrate  the  glass,  and  the 
other  to  be  reflected  from  it.  At 
a  certain  angle,  called  the  angle 
of  complete  polarization,  this  ten- 
dency produces  a  complete  sepa- 
ration of  the  two  components  of 
the  ray.  One  component,  as 
shown  in  Fig.  376,  penetrates  the  material  of  the  mir- 
ror, and  is  transmitted  as  a  refracted  ray ;  the  other  is 
reflected.  This  reflected  ray  contains  only  vibrations  in 
one  plane.  It  constitutes  what  is  called  a  beam  of  plane 
polarized  light.  To  show  that  it  consists  of  vibrations  in 
a  single  plane  only,  a  second  mirror  may  be  interposed  in 
its  path  at  the  angle  of  polarization.  If  this  mirror  be 
turned,  as  shown  in  Fig.  377,  it  will  reflect  the  polarized 


FIG.  376. 


404  THE  OUTLINES   OF  PHYSICS 

ray  because  the  vibrations  meet  its  surface  in  the  same 
manner  as  in  the  case  of  the  first  mirror.  If,  however,  it 
be  turned  through  90°,  the  ray  will  enter  the  mirror,  and 


FIG.  377. 


there  will  be  no  reflected  ray.  For  this  experiment,  it  is 
necessary  to  use  mirrors  in  which  the  reflection  occurs 
from  the  front  surface  only.  The  most  suitable  material 
is  black  glass,  in  which  the  refracted  ray  is  entirely  ab- 
sorbed. A  metallic  reflecting  surface  does  not  polarize 
light  as  above  described. 

371.  Polarization  by  Means  of  Double  Refraction.  —  Cer- 
tain crystals  are  so  constituted  that  the  velocity  of  light 
transmitted  by  them  depends  upon  the  plane  of  its  vibra- 
tion. If  a  beam  of  ordinary  light  enter  such  a  crystal,  it 
will  be  resolved  into  two  components,  which  will  vibrate  at 
right  angles  to  one  another.  These  two  rays  will  travel 
through  the  crystal  at  different  velocities.  One  of  them, 
therefore,  will  be  relatively  retarded,  and  will  fall  behind 
the  other.  If  the  beam  of  light  enter  the  crystal  obliquely, 
the  ray  which  is  most  retarded  will  be  bent  further  from 
its  path  than  the  other,  and  the  two  beams,  on  emerging, 
will  follow  different  paths.  (See  Fig.  378.)  Every  such 
crystal  divides  the  light  which  it  transmits  into  two  op- 


POLARIZATION  AND  DOUBLE  REFRACTION       405 

positely  polarized  rays,  one  of  which  is  called  the  ordinary, 
and  the  other,  to  distinguish  it,  the  extraordinary,  ray. 
The  phenomenon  is  called  double  refraction. 


FIG.  378. 

372.  The  Nicol  Prism.  —  In  order  to  obtain  a  single 
plane  polarized  ray  by  double  refraction,  it  is  necessary  to 
suppress  one  of  the  rays  within  the  crystal.  This  is  done 
by  means  of  a  device  known  as  the  Nicol  prism. 

A  rhomb  of  Iceland  spar,  which  is  a  doubly  refracting 
substance,  is  cut  obliquely  through,  and  cemented  by 
means  of  Canada  balsam.  The  position  of  the  surface  thus 
formed  is  such  that  the  ordinary  ray  is  totally  reflected, 
while  the  extraordinary  ray  is  transmitted.  (See  Fig.  379.) 
In  this  way,  a  single  beam  of  polar- 
ized light  is  obtained,  the  vibration 
of  which  depends  upon  the  position 
of  the  prism,  and  turns  with  it. 
Polarized  light  entering  a  Nicol 

prism,  if  vibrating  in  the  plane  of  the  extraordinary 
ray,  will  be  transmitted ;  if  vibrating  in  the  plane  of  the 
ordinary  ray,  it  will  be  extinguished.  Light  which  vibrates 
in  any  intermediate  plane  is  resolved  into  two  components; 
one  of  which  takes  the  plane  of  vibration  of  the  extraor- 
dinary ray,  the  other  that  of  the  ordinary  ray.  The 
former  component  only  is  transmitted.  Ordinary  light  is 
likewise  resolved  into  the  two  above-mentioned  compo- 
nents, and  is  converted  into  polarized  light. 

In  the  study  of  polarization,  two  Nicol  prisms  are  com- 


406 


THE  OUTLINES   OF  PHYSICS 


monly  used ;  the  first  of  these  is  called  a  polarizer ;  the 
second,  an  analyzer.  (See  Fig.  380.)  They  are  mounted 
with  a  common  axis  about  which  each  is  capable  of  revo- 
lution. Such  an  arrangement  is  called  a  polariscope. 


FIG.  380. 

373.  EXPERIMENT  119.  —  Double  Refraction  in  Calcite. 

Apparatus  : 

(1)  The  lantern. 

(2)  A  pair  of  Nicol  prisms. 

(3)  A  rhomb  of  calcite. 

Procedure  : 

(a)  -Place  before  the  condenser  of  the  lantern  the  diaphragm  with 
circular  opening  previously  described,  and  focus  the  image  of  the 
same  upon  the  screen.  Mount  between  the  diaphragm  and  the  objec- 
tive the  rhomb  of  calcite  r,  as  shown 
in  Fig.  381.  Note  that,  owing  to 
double  refraction  in  the  crystal,  two 
images  appear. 

(b)  Hold  one  of  the  Nicol  prisms 
between  the  calcite  rhomb  and  the 
objective,  and  turn  it  in  the  hand,  the 
axis  of  rotation  in  the  path  of  the  ray. 
Note  that  in  certain  positions  of  the 
Nicol  prism  one  of  the  images  is 

entirely  extinguished,  while  the  other  appears  undimmed,  and  that 
by  turning  the  Nicol  prism  further  through  45°  both  images  appear 
of  equal  brightness.  Note  that  a  further  revolution  through  45° 
extinguishes  the  other  image,  and  so  on  until  the  circle  is  completed. 

The  interpretation  of  this  result  follows  directly  from  the  foregoing- 
discussion  of  double  refraction.  The  two  images  are  formed  by  rays 
of  light  which  are  polarized,  one  at  right  angles  to  the  other.  When 
the  plane  of  polarization  of  the  Nicol  prism  corresponds  with  the 
plane  of  vibration  of  one  of  these  rays,  that  ray  is  transmitted  while 
the  other  is  extinguished.  In  the  position  45°  from  this,  both  rays 


a 


FIG.  381. 


POLARIZATION  AND  DOUBLE  REFBACTION        407      • 

are  resolved  into  components,  one  of  which  is  transmitted  and  the 
other  extinguished ;  thus  two  rays  appear,  and  of  equal  brightness. 

(c)  Hold  the  Nicol  prism  between  the  diaphragm  and  the  calcite 
rhomb  and  turn  as  before.     In  this  case  we  have  a  single  polarized 
ray  passing  through  the  crystal.     This  is  resolved  into  components 
vibrating  in  the  planes   of  the   ordinary  or  extraordinary  rays  in 
calcite.     There  are,  however,  two  positions  in  which  one  of  these  com- 
ponents becomes  equal  to  zero,  and  two  in  which  the  other  component 
is  destroyed.     In  these  four  positions  a  single  image  only  appears ;   in 
intermediate  positions  both  images  are  present,  their  relative  bright- 
ness depending  upon  the  size  of  the  respective  components. 

(d)  Remove  the  calcite  prism  and  place  the  two  Nicol  prisms  in 
the  path  of  the  ray.     Turn  one  of  these  until  their  planes  of  polariza- 
tion form  a  right  angle  with  one  another.     The  polarized  ray  pro- 
duced by  the  polarizer  is  now  incapable   of  passing  through  the 
analyzer,  and  no  image  of  the  aperture  appears.     Nicol  prisms  in 
these  positions  are  said  to  be  crossed.    As  we  turn  the  analyzer  slowly 
from  this  position,  the  image  reappears,  increasing  in  brightness  to  a 
maximum  when  the  planes  of  polarization  of  the  two  prisms  coincide.1 
Having  crossed  the  Nicol  prisms,  insert  the  calcite  crystal  between 
and  note  the  restoration  of  light  to  the  field  of  view. 

Anything  which  changes  the  plane  of  vibration  of  the  light  entering 
the  analyzer,  so  that  it  does  not  vibrate  at  right  angles  to  the  plane  of 
polarization  of  that  prism,  will  cause  light  to  be  transmitted  to  the 
screen.  Any  double  refracting  substance,  of  which  there  are  many, 
interposed  between  the  Nicol  prisms,  will  have  this  effect.  Plates 
of  mica,  selenite,  quartz,  calcite,  etc.,  etc.,  if  held  between  the  Nicol 
prisms,  will  answer  for  this  purpose.  There  is,  indeed,  no  simpler 
method  of  determining  whether  a  substance  is  doubly  refracting  than 
to  place  a  piece  of  it  between  crossed  Nicol  prisms.  Many  liquids, 
such  as  solutions  of  sugar  and  of  tartaric  acid,  produce  a  similar 
effect,  not  because  they  are  capable  of  double  refraction,  but  because 
they  have  power  of  rotating  the  plane  of  light  transmitted  through 
them.  In  the  case  of  sugar  this  property  is  utilized  for  determining 
the  strength  of  the  solution.  A  polarizer  arranged  for  this  purpose 
is  called  a  sac  char  imeter. 

1  The  brightness  of  the  image  is  proportional  to  cos2  a,  where  a  is  the 
angle  between  the  planes  of  polarization  of  the  Nicol  prisms. 


408  THE  OUTLINES   OF  PHYSICS 

374.  EXPERIMENT  120.  —  Double  Refraction  produced  by  Stress. 

Apparatus : 

(1)  The  lantern. 

(2)  A  pair  of  Nicol  prisms ;   a  block  of  plate  glass,  about  4  cm. 
square  ;  an  iron  clamp. 

Procedure  : 

(a)  Set  up  the  Mcol  prisms  between  the  condenser  and  the 
objective  lens  of  the  lantern  and  cross  them.  Hold  the  block  of  plate 
glass  between  the  Nicol  prisms,  and  note  that  no  effect  is  produced 
thereby. 

(6)  Place  the  block  of  glass  in  the  jaws  of  the  clamp  so  that  pres- 
sure may  be  applied  at  the  center  of  opposite  edges;  hold  it  thus 
clamped  in  the  field  and  increase  the  pressure  by  turning  the  screw  of 
the  clamp.  Note  that  light  appears  in  the  field  of  the  crossed  Nicol 
prism,  with  a  beautiful  colored  pattern  due  to  interference  of  the 
transmitted  rays.  Relieve  the  pressure,  and  note  that  the  glass 
returns  to  its  former  condition.  Similar  effects  may  be  produced  by 
holding  a  strip  of  glass  in  the  field  and  bending  it.  Also  by  clamping 
a  glass  rod  or  tube  horizontally  so  that  one  end  passes  through  the 
field  of  the  lantern.  If  this  rod  be  rubbed  longitudinally  with  the 
moistened  hand,  so  as  to  cause  it  to  vibrate,  it  will  be  strained  in 
such  a  way  as  to  produce  total  refraction  and  to  cause  light  to  pass 
the  polarizer. 

375.  The  Interference   of  Light  Waves.  —  Two  rays   of 
light  of   the  same  wave  length,  moving  along  the   same 
path  in  the  same  direction,  produce  a  motion  of  the  ether 


FIG.  382. 


which  is  the  resultant  of  the  two  separate  motions  due 
to  the  two  waves.  If  the  two  waves  are  vibrating  in  the 
same  plane  and  in  the  same  phase  (see  Fig.  382),  the 


POLARIZATION  AND  DOUBLE  EEFEACTION       409 

resultant  motion  will  be  the  sum  of  the  two.  If  the  two 
waves  are  of  opposite  phase  (see  Fig.  383)  and  are  equally 
bright,  their  motions  will  annul  each  other,  and  the 


FIG.  383. 

resultant  motion  of  the  ether  will  be  their  difference. 
In  the  latter  case,  when  the  amplitudes  are  equal,  dark- 
ness is  produced. 

This  combination  of  the  motions  of  two  light  waves  to 
produce  darkness  is  called  interference.  It  forms  the  basis 
of  many  very  beautiful  optical  phenomena,  of  which  only 
a  few  of  the  simplest  can  be  described  here. 

376.  EXPERIMENT  121.  —  Colors  of  the  Soap  Film,  produced  by 
Interference. 

Apparatus : 

(1)  A  flat  dish  containing  a  soap  solution. 

(2)  A  lamp  chimney  of  the  form  shown  in  Fig.  384. 
Procedure :  -* 

(a)  Dip  the  base  of  the  chimney  into  the  soap  solution 
and  remove  it  carefully.  The  film  which  stretches  itself 
across  the  base  of  the  chimney,  and  which  can  be  re- 
moved with  it,  immediately  finds  its  way  to  the  nar- 
rowest part  of  the  base,  where  it  forms  a  plane  dia- 
phragm. 

(6)  Set  up  the  chimney  so  that  the  soap  film  will  be  in  a  vertical 
position,  and  observe  the  changes  which  it  undergoes.  The  film,  at 
first  colorless,  grows  thinner  by  the  evaporation  of  its  particles  and  by 
a  process  of  drainage,  in  consequence  of  which  the  liquid  flows  down- 
ward under  the  action  of  gravity  and  escapes.  Very  soon  colors 
begin  to  show  themselves  in  the  upper  portion  of  the  film,  and,  if 
the  latter  remain  undisturbed,  these  colors  will  arrange  themselves 
in  parallel  horizontal  bands  which  move  slowly  downward  until  the 


Fia.  384. 


410  THE  OUTLINES  OF  PHYSICS 

entire  surface  is  covered  with  them.  As  time  goes  on,  new  ones  appear 
continually  at  the  top  of  the  film  and  join  in  this  downward  move- 
ment. Finally,  if  the  film  is  not  broken,  the  upper  portion  changes 
color  again  to  a  neutral  gray,  sometimes  almost  black,  and  no  more 
colored  bands  are  formed.  Note  that  the  bands  follow  the  order  of 
the  colors  of  the  spectrum,  running  from  red  to  violet.  The  explana- 
tion of  these  phenomena  is  as  follows  : 

The  rays  which  fall  upon  the  film  are  reflected  from  the  front  and 
from  the  back  surface.  A  ray  a,  b  (Fig.  385),  which  passes  through 
the  film  and  is  reflected  from  the  back  surface, 
afterwards  traveling  along  a  common  path  d,  e, 
with  a  ray  c,  d,  reflected  from  the  front  surface, 
has  had  a  longer  distance  to  travel,  and  differs 
from  the  latter  ray  in  phase.  If  the  distance 
through  the  film  and  back  again  is  such  that  the 
two  reflected  rays  are  in  opposite  phase,  they 
destroy  each  other.  Any  very  thin  film  that 
reflects  light  from  its  two  surfaces  will  produce 
complete  interference  between  light  of  some  given 
wave  length.  Other  wave  lengths  will  not  inter- 
fere completely.  If  the  ray  which  falls  upon  the 
film  consists  of  white  light,  that  which  is  returned 
from  it  will  be  white  light  minus  some  color  which  has  been  destroyed 
by  interference.  The  result,  therefore,  of  interference  in  the  case  of 
the  soap  bubble  and  of  other  thin  films  is  to  produce  variations  of 
color  instead  of  mere  gradations  of  light  and  shade.  Owing  to  the 
vertical  position  of  the  film  and  the  action  of  gravity  upon  it,  the 
liquid  tends  to  the  bottom,  giving  the  film  a  wedge-shaped  cross-sec- 
tion. It  is,  therefore,  always  thinnest  at  the  top.  As  we  go  from  the 
top  downward  with  the  increasing  thickness,  the  different  colors  of 
the  spectrum  are  caused  to  interfere,  and  the  result  is  the  arrange- 
ment of  the  colors  in  horizontal  bands  as  above  described.  Anything 
which  stirs  up  the  liquid  within  the  film,  which  may  be  done  by 
blowing  upon  it  gently,  will  destroy  this  arrangement,  mixing  the 
colors  up  temporarily.  Upon  being  allowed  to  rest,  the  old  arrange- 
ment of  bands  re-establishes  itself.  The  neutral  color,  which  the  film 
finally  assumes  before  breaking,  is  due  to  the  fact  that  it  has  become 
so  thin,  as  compared  with  the  wave  length  of  light,  that  there  is  not 
a  sufficient  difference  of  phase  between  the  waves  reflected  at  its  two 
surfaces  to  cause  interference. 


POLARIZATION  AND  DOUBLE  REFRACTION       411 

(c)  Repeat  the  above-described  observations  in  a  darkened  room, 
using  as  the  sole  source  of  illumination  a  sodium  flame.  Note  that 
the  interference  bands  are  now  alternately  black  and  yellow.  Those 
regions  in  the  film,  the  thickness  of  which  is  such  as  to  produce  oppo- 
site phases  in  the  waves  of  sodium  light,  appear  black ;  those  regions 
where  the  thickness  is  such  as  to  give  the  same  phase  in  the  waves 
reflected  from  the  two  surfaces  possess  the  greatest  brightness. 

377.  Interference  Colors  in  Nature.  —  Many  of  the  most 
beautiful  color  effects  in  nature  are  produced  by  inter- 
ference of  the  light  reflected  from  thin  films.     The  pearl, 
the  opal,  and  other  gems  owe  their  colors  to  interference. 
The  coloring  of  many  insects  and  of  the  plumage  of  some 
birds,  also  the  coloring  of  the  linings  of  shells,  is  ascribable 
to  the  same  cause.     All  the  effects  included  under  the 
term  iridescence  are  due  to  interference. 

378.  Newton's  Rings.  —  Another  case  of  the  interference 
of  light  is  that  produced  when  a  lens  is  laid  upon  a  plane 
glass  plate,  or  when  two  lenses  differing  in  curvature  are 

brought    together.     If  the   surfaces   be    ^-- — 7 

thoroughly  cleaned   so  that   they  come    i  -^^ — 

well    together,   interference    occurs    be-   L 


tween  the  light  reflected  from  the  inner  FlQ-  386- 

surface  of  the  upper  lens  and  the  upper  surface  of  the 
glass  beneath.  The  intervening  path  through  the  air  in- 
creases as  we  pass  from  the  center  where  the  glass  surfaces 
are  in  actual  contact  outwards  (Fig.  386).  The  result  is 
a  series  of  circular  interference  bands  following  the  order 
of  the  colors  of  the  spectrum.  These  are  known  as 
Newton's  rings. 

Whenever  two  glass  surfaces,  which  do  not  fit  each  other 
precisely,  are  brought  together,  interference  bands  show 
themselves.  If  the  surfaces  be  irregular,  these  take  on 


412  THE  OUTLINES  OF  PHYSICS 

irregular  forms.  If  two  surfaces  could  be  made  which 
fitted  each  other  precisely,  so  that  the  distance  between 
them  was  everywhere  the  same,  the  interference  color 
would  be  uniform  for  the  entire  surface.  This  fact  affords 
an  exceedingly  delicate  means  of  testing  the  precision  with 
which  glass  surfaces  are  ground.  If  two  plates  which  fit 
each  other  very  perfectly  are  laid  one  upon  the  other,  the 
interference  bands  will  run  across  nearly  in  straight  lines, 
and  will  be  very  broad.  If  now  the  finger  be  placed  upon 
the  upper  plate  with  slight  pressure  for  a  moment,  this 
pressure  will  be  sufficient  to  distort  the  upper  plate  and 
throw  these  bands  out  of  shape  and  position.  Upon  re- 
moving the  finger,  the  effect  is  found  to  remain  after  the 
pressure  is  relieved,  owing  to  the  distortion  of  the  upper 
plate  on  account  of  unequal  heating.  The  interference 
fringes  require  several  minutes  to  return  to  their  original 
position  again.  The  observation  should  be  made  by  sodium 
light,  because  the  number  and  sharpness  of  the  bands  is 
thus  greatly  increased. 

379.  Interference  Phenomena  in  Polarized  Light.  —  When 
a  double  refracting  crystal  is  placed  between  crossed  Nicol 
prisms,  as  described  in  the  foregoing  chapter,  and  the  light 
is  thus  restored,  colors  frequently  show  themselves.  These 
are  due  to  the  interference  of  the  ordinary  with  the  ex- 
traordinary ray.  These  have  difference  of  phase  owing  to 
the  fact  that  their  velocities  in  the  crystal  differ  from  one 
another.  Crystals  of  different  thicknesses  bring  different 
colors  into  interference.  Thus  a  bit  of  mica  which  is  made 
up  of  overlapping  layers  or  plates,  and  which  is  not  uni- 
form in  thickness,  will  frequently  show,  when  placed  be- 
tween the  Nicol  prisms,  a  complicated  field  of  various 
colors. 


VISION  AND   THE  SENSE  OF  COLOR  413 


CHAPTER   XLIII 
VISION  AND  THE  SENSE  OF  COLOR 

380.  Essential  Parts  of  the  Eye.  —  The  eye  consists  of  a 
nearly  circular  chamber,  the  eyeball,  within  a  round  open- 
ing, in  front  of  which  is  a  lens  (Fig.  387).  By  means  of 
this  lens  real  images  of  objects  before  the  eyes  are  thrown 
upon  a  sort  of  screen 
or  background,  which  is 
called  the  retina.  The 
retina  consists  of  a  net- 
work of  nerve  fibers  of  ^^^^"  Mi- 
very  complicated  struc- 
ture which  form  the  ends 

of  the  optic  nerve.    This 

r  FIG.  387. 

bundle  of  nerves  extends 

from  the  brain  to  the  eye,  and  enters  the  latter  through 
an  opening  at  the  back.  Thence  the  nerve  fibers  spread 
out  over  the  interior  of  the  eyeball,  forming  the  retina. 

In  order  to  bring  near  and  distant  objects  to  an  equally 
good  focus  upon  the  retina  without  changing  the  distance 
between  the  lens  and  the  image,  the  lens  itself  is  made  to 
change  its  form  by  means  of  a  ring  of  muscles  surrounding 
it.  This  process  is  called  accommodation.  When  distant 
objects  are  to  be  brought  to  a  focus,  these  muscles  contract, 
stretching  the  lens  radially,  and  thus  making  it  thinner 
and  increasing  its  focal  length.  To  see  objects  near  at 
hand,  which,  in  this  stretched  condition  of  the  lens  would 
be  brought  to  a  focus  too  far  back,  the  focal  length  of  the 


FAR  SIGHTED  EYE 


414  THE  OUTLINES   OF  PHYSICS 

lens  must  be  diminished.  This  is  done  simply  by  relaxing 
the  muscles  of  accommodation.  In  the  normal  eye  in  youth 
the  process  of  accommodation  makes  it  possible  to  see  with 
equal  sharpness  objects  15  or  20  cm.  distant  from  the  eye 
and  those  miles  away.  With  advancing  age  the  power  of 
accommodation  diminishes,  and  as  a  rule  the  focus  is  better 
for  distant  than  for  near  objects.  This  lack  of  accommo- 
dation is  made  good  by  the  use  of  spectacles. 

381.   Near  and  Far  Sightedness.  —  In  many  eyes  the  focal 
length  of  the  lens  is  somewhat  too  great.     Persons  whose 

eyes  have  this  peculiarity 
are  said  to  be  far-sighted. 
They  can  see  distant  ob- 
jects sharply  defined,  but 
the  power  of  accommoda- 
tion does  not  bring  objects 
near  at  hand  into  focus. 

This  difficulty  is  remedied  by  the  use  of  a  convex  lens  in 
front  of  the  eye.  (See  Fig.  388.)  In  other  persons  the  focal 
length  of  the  lens  is  too  short,  and  only  objects  quite  close 

at  hand  can  be  brought 
to  a  focus  by  the  use  of 
the  muscles  of  accommo- 
dation. The  attempt  to 
adjust  the  eye  continu- 
ally to  objects  farther 

away  produces  serious  nervous  strain.  The  use  of  glasses 
is  therefore  very  important  in  cases  of  near-sightedness. 
The  lens  to  be  used  is  one  which  will  increase  the  focal 
length,  namely,  a  divergent  lens  (Fig.  389). 

In  order  that  the  lens  of  the  eye  may  be  capable  of 
changing  form  under  the  action  of  the  muscles  of  accommo- 


VISION  AND   THE  SENSE  OF  COLOR  415 

dation,  it  is  kept  moist  by  the  liquids  which  fill  the  eyeball. 
These  are  called  the  humors  of  the  eye.  That  between 
the  retina  and  the  lens  is  called  the  vitreous  humor.  In 
front  of  the  lens  is  the  aqueous  humor.  It  is  held  in  place 
by  the  cornea,  a  convex  window  not  unlike  a  watch  glass 
in  shape.  The  cornea  is  a  transparent  continuation  of 
the  coat  of  the  eyeball  called  the  sclerotic  coat.  Between 
the  lens  and  the  cornea  is  a  colored  diaphragm  with  a 
central  circular  aperture.  This  diaphragm  is  the  iris  and 
the  opening  is  the  pupil  of  the  eye.  The  iris  serves  the 
same  purpose  as  the  adjustable  diaphragm  in  the  lens  of  a 
camera.  It  regulates  the  amount  of  light  falling  upon  the 
retina,  and  by  "  stopping  down  "  the  lens  greatly  increases 
the  sharpness  of  vision.  It  contains  a  set  of  radial  muscle 
fibers,  which  by  their  involuntary  action  continually  adjust 
the  opening  to  suit  the  conditions  of  illumination. 

The  eye  is  moved  chiefly  by  means  of  four  muscles 
attached  to  the  sclerotic  coat.  Two  of  these,  which  are 
attached  above  and  below  by  means  of  the  tendons  shown 
in  Fig.  387,  give  the  eye  motion  in  a  vertical  plane.  The 
other  pair  enable  us  to  move  the  eye  in  a  horizontal  plane. 

382.  The  Region  of  Distinct  Vision.  —  Although  the  retina 
covers  a  large  portion  of  the  interior  of  the  eyeball,  it  is 
only  a  small  region  directly  in  the  axis  of  the  lens  which 
gives  distinct  vision.  The  process  of  seeing  consists  in 
moving  the  eye  continually,  by  means  of  its  muscles,  so  as 
to  bring  different  portions  of  the  image  of  the  object  at 
which  we  are  looking  into  this  region  of  distinct  vision. 
Were  the  eye  incapable  of  such  movement,  we  should  get 
no  distinct  impressions  concerning  portions  of  the  image 
which  lay  outside  this  region  of  distinct  vision. 

In  order  to  test  this  point,  it  is  only  necessary  to  fix  the 


416 


THE  OUTLINES   OF  PHYSICS 


eye  upon  one  end  of  a  printed  line  in  the  middle  of  a  page 
of  a  book  held  about  20  cm.  away.  It  will  be  found  im- 
possible to  read  half  across  the  line,  although  we  have  an 
indefinite  impression  of  the  presence  of  the  remaining 
words.  It  will  be  found  in  the  same  way  that  if  we 
look  at  the  upper  line  of  a  page,  and  are  successful  in 
preventing  the  tendency  of  the  eye  to  fall  in  the  direc- 
tion to  which  our  attention 
is  directed,  the  third  line 
below  cannot  be  read. 

The  movements  of  the  eye, 
above  described,  which  are. 
purely  automatic,  constitute 
a  process  of  measuring  the 
angular  distances  between 
different  parts  of  the  image. 
From  these  measurements  we 
get  our  estimate  of  shape 
and  size,  and  from  them  in- 
directly, in  the  case  of  famil- 
iar objects,  the  size  of  which 
is  known  to  us,  we  estimate 
distance.  From  our  judg- 
ment as  to  the  distance  of 
Fia  390<  the  object  on  the  other  hand, 

we  estimate  its  size. 

The  influence  of  our  estimate  of  distance  upon  our  judg- 
ment concerning  the  relative  sizes  of  things  is  illustrated 
in  Fig.  390,  in  which  the  three  human  figures  are  all  of 
the  same  height.  The  perspective  is  so  arranged,  how- 
ever, as  to  make  them  seem  at  different  distances,  and  the 
observer  unconsciously  assigns  to  each  a  size  proportionate 
to  its  apparent  distance. 


VISION  AND   THE  SENSE  OF  COLOR  417 

383.  Binocular  Vision.  —  In  the  matter  of  estimating  size 
and  distance,  we  are  greatly  aided  by  having  two  eyes 
situated  some  little  distance  apart.     The  consequence  is 
that  we  get  two  slightly  different  views  of  the  object,  and 
our  best  means  of  judging  distances  is  by  comparison  of 
these.    The  process  of  viewing  objects  simultaneously  with 
both  eyes  is  called  binocular  or  stereoscopic  vision. 

The  extent  to  which  we  are  dependent  upon  stereo- 
scopic vision,  in  our  estimate  of  the  position  of  things, 
may  be  illustrated  by  means  of  the  following  very  simple 
experiment : 

Close  one  eye,  and  approach,  from  some  distance,  an 
object  like  the  edge  of  a  table.  When  within  easy  arm's 
reach,  attempt  to  place  the  point  of  a  pencil,  held  in  the 
hand,  in  contact  with  the  object  in  question.  It  will  be 
found  impossible  to  do  so  until,  after  successive  trials,  the 
distance  has  been  gauged  by  means  of  the  motion  of  the 
arm.  With  two  eyes,  however,  the  point  may  be  touched 
at  the  first  attempt. 

384.  Color.  —  Color  is  produced  by  any  process  which 
modifies  the  composition  of  white  light.     When  light  is 
dispersed,  forming  a  pure  spectrum,  each  ray  possesses  its 
individual  color.     Colors  thus  produced  are  called  spectral 
tints.     In  nearly  all  cases,  however,  bodies  owe  their  color 
to  the  removal  of  some  portion  of  white  light,  either  by 
interference  or  by  absorption.     The  production  of  color  by 
interference  has  already  been  considered.     (See  Chapter 
XLII.)     Nearly  all  cases  of  the  production  of  color  fall 
under  the  second  head,  namely,  absorption.     When  light 
falls  upon  a  colored  object,  such  as  a  pigment,  the  rays 
which  penetrate  the  body  are  reflected  from  within.    These 
rays  suffer  absorption,  but  some  wave  lengths  are  more 


418 


THE  OUTLINES   OF  PHYSICS 


diminished  in  intensity  than  others.  The  remaining  light 
produces  an  effect  upon  the  eye  other  than  white,  and 
gives  the  body  its  characteristic  color.  Thus  a  pigment 
like  red  lead  absorbs  nearly  all  the  shorter  wave  lengths, 

and  only  red  light,  with  an 
admixture  of  yellow,  is  trans- 
mitted. Green  pigments  are 
produced  by  the  absorption 
of  both  red  and  violet,  blue 
by  the  absorption  of  the  red 
and  green. 

Measurements  of  the  differ- 
ent wave  lengths  reflected  by 
three  typical  pigments,  and 
expressed  graphically  by 
means  of  curves,  are  shown 
in  Fig.  391.  None  of  the 
colors  produced  in  these  cases 
are  pure  ;  that  is  to  say,  there 
is,  in  all  cases,  a  considerable 
admixture  of  light  other  than 
that  which  gives  the  prevailing  color  tone.  Purity  of  color 
denotes  absence  of  these  admixtures.  The  only  perfectly 
pure  colors  are  those  of  the  spectrum  formed  by  a  narrow 
slit.  Colors  differ  also  in  saturation.  This  term  denotes 
the  absence  of  admixture  of  white  light.  In  proportion  as 
the  white  light  is  done  away  with,  and  the  tint  becomes 
more  and  more  intense,  it  is  said  to  be  more  and  more 
saturated.  There  is,  in  all  ordinary  cases,  a  considerable 
amount  of  white  light  present  in  the  rays  reflected  by 
pigments,  because  not  all  the  light  penetrates  the  sub- 
stance, and  thus  a  considerable  portion  is  reflected  from 
the  surface,  and  this  does  not  suffer  absorption. 


ABC 


VISION  AND   THE  SENSE  OF  COLOR  419 

385.  Dependence  of  Color  upon  the  Character  of  the  Incident 
Light.  —  Colored  objects  are  capable  of  modifying  the  light 
which  falls  upon  them  only  by  process  of  absorption.    They 
can  therefore  reflect  back  no  rays  which  do  not  reach  them. 
The  colors  which  they  present  contain  no  light  which  has 
not  been  thrown  upon  them  from  without.     In  proportion 
as  the  source  of  illumination  is  rich,  the  effect  will  be 
varied  upon  the  bodies  which  it  illuminates.      Daylight, 
for  example,  is  richer  in  violet  and  blue  rays  than  any 
artificial  light.     Colors  seen  by  daylight,  therefore,  send 
the  eye  a  larger  proportion  of  these  tints.    If,  for  daylight, 
we  substitute  gaslight,  which  is  comparatively  weak  in 
violet  ra}^s,  objects  of  a  bluish  cast  tend  towards  green. 
Differences  in  the  color  of   bodies,  which  are   perfectly 
obvious  by  daylight,  are  scarcely  to  be  distinguished  when 
the  bodies  are  seen  by  lamplight.     If,  for  lamplight,  we 
substitute,  in  turn,  the  sodium  flame,  which  possesses  only 
one  color,  yellow,  we  find  all  pigments,  whatever  may  be 
their  colors  by  daylight,  reduced  to  a  mixture  of  yellow 
and  black.     This  may  be  strikingly  illustrated  by  taking 
a  pile  of  colored  worsteds  containing  a  large  number  of 
different  tints  (the  collection  used  in  the  Holmgren  test 
for  color  blindness    [Art.  390]  is  well  adapted  for  this 
experiment),  and  viewing  them,  first  by  daylight,  and  then 
in  a  perfectly  darkened  room,  by  the  light  of  the  sodium 
flame.     The  matter  of  the  dependence  of  color  upon  the 
source  of  illumination  may  be  more  definitely  brought  out 
by  means  of  the  following  experiment : 

386.  EXPERIMENT  122.  —  Observation  of  Pigment  Colors  by  Means 
of  the  Spectrum. 

Apparatus  : 

(1)  The  lantern  with  lens  and  prism. 


420  THE  OUTLINES   OF  PHYSICS 

(2)  Holmgren  worsteds,  or  any  other  collection  of  brightly  colored 
objects. 

Procedure : 

(a)  Adjust  the  lens  and  prism  so  as  to  project  a  spectrum  upon  the 
screen.  Darken  the  room  completely. 

(&)  Select  a  skein  of  scarlet  worsted,  and  move  it  slowly  through 
the  spectrum  from  red  to  violet.  Note  that,  while  illuminated  by  the 
red  rays  of  the  spectrum,  it  appears  in  its  natural  tint  and  very  bright. 
As  it  passes  out  of  the  red  into  the  orange,  it  grows  rapidly  darker  in 
color.  When  the  green  is  reached,  the  worsted  has  become  black,  nor 
does  it  resume  its  natural  lively  tint  again  in  passing  through  any  of 
the  shorter  wave  lengths  of  the  spectrum.  This  worsted  absorbs 
nearly  all  the  wave  lengths  of  the  spectrum  excepting  those  at  the 
red  end.  It  appears  black,  except  when  illuminated  by  rays  which  it 
is  capable  of  transmitting. 

(c)  Repeat,  using  a  piece  of  green  worsted,  and  note  that,  at  the 
red  end  of  the  spectrum,  this  appears  very  dark,  and  that  it  grows 
rapidly  brighter  when  moved  through  the  yellow  into  the  green.     It 
retains  some  portion  of  its  brightness  throughout  the  blue.    Specimens 
of  blue  worsted,  or  of  any  artificially  blue  body,  tested  thus  will  show, 
as  a  rule,  some  power  of  reflecting  red   light.      They  will  appear 
brighter  when  illuminated  by  the  red  than  by  the  yellow  or  green. 
It  is  only  in  the  blue  and  violet  light,  however,  that  they  take  on 
their  usual  appearance.     There  are  scarcely  any  pure  blues  among 
pigments.     Nearly  all  are  purples ;   that  is  to  say,  they  reflect  a  con- 
siderable percentage  of  red  light  as  well  as  of  blue. 

(d)  Repeat  the  above-described  observations,  using  a  fresh  blade 
of  grass.     The  coloring  matter  of  this  is  chlorophyl,  the  spectrum  of 
which  has  already  been  described  in  Experiment  113.     Although  the 
dominant  color  tone  of  grass  is  green,  not  all  the  wave  lengths  of  red 
are  absorbed  by  it.    As  we  move  the  blade  of  grass  through  the  spec- 
trum, we  find  that  it  is  capable  of  reflecting  quite  strongly  in  certain 
regions  of  the  red,  and  becomes  suddenly  black  in  passing  into  others ; 
the  latter  are  the  regions  of  the  absorption  bands  of  chlorophyl. 

387.  The  Theory  of  Color  Sensations.  —  To  understand 
the  different  sensations  produced  upon  the  mind  by  differ- 
ent wave  lengths  of  light,  it  is  necessary  to  consider  the 


VISION  AND   THE  SENSE  OF  COLOR 


421 


process  by  which  impressions  of  color  are  acquired.  -  The 
ray  entering  the  eye  falls  upon  the  retina,  and  excites 
the  ends  of  the  fibers  of  the  optic  nerve,  which  are  spread 
out  in  the  form  of  a  network  within  the  eye.  By  means 
of  the  excitation  of  these  nerves,  messages  are  sent  to  the 
brain. 

Various  theories  have  been  proposed  to  account  for  the 
different  sensations  produced  by  the  action  of  different  wave 
lengths  of  the  spectrum.  The  simplest  of  these,  and  the 
one  usually  adopted  by  physicists  as  a  working  hypothesis 
for  the  explanation  of  color  phenomena,  is  known  as  the 
Young-Helmholtz  Theory  of  Color. 

According  to  this  theory,  there  are  in  the  retina  three 
distinct  sets  of  nerves  :  one  of  which  conveys  the  sensation 
of  red,  another  the  sensation  of  green,  and  the  third  a  sen- 
sation of  violet  to  the  brain.  We  may  call  these  nerves 
the  red  nerve,  the  green  nerve,  and  the  violet  nerve.  The 
sensations  which  they  produce,  i.e.  red,  green,  and  violet, 
are  called  the  three  primary  color  sensations.  By  the  com- 
bination of  them,  all  known  color  sensations  may  be  pro- 
duced. It  has  been  found  that  a  trained  observer  can 
distinguish  about  ten  thousand  differences  of  color,  com- 
paratively few  of  which  have  received  names.  Every  one 
of  these  may  be  formed  R  o  Y  n  R  v 
by  an  admixture  of  the 
three  primary  colors  in 
proper  proportions.  The 
red  nerve  is  chiefly  af-  _ 
fected  by  the  longer  FIG.  392. 

wave  lengths  of  the  spectrum.     Objects,  ther/ 
send  such  rays  to  the  eye  give  us  the  imj/ 
we  call  red.     All  wave  lengths  have   s 
ever,  upon  these  nerves.     If  we  could  i 


422 


THE  OUTLINES   OF  PHYSICS 


R      0 


FIG.  393. 


of  red,  and  test  our  color  sense  by  subjecting  the  red 
nerve  successively  to  the  different  wave  lengths  of  the  spec- 
trum, we  should  be  able  to  express  the  intensity  of  the 
effect  by  means  of  a  curve,  as  shown  in  Fig.  392.  In  the 
same  way  the  green  nerve  is  sensitive  to  all  the  wave 

lengths  of  the  spectrum, 
but  chiefly  to  those  which 
lie  in  the  region  which 
we  call  green..  The  ef- 
fect of  different  wave 
_  lengths  upon  it  would 
be  expressed  by  the  cor- 
responding curve  (Fig.  393).  The  effect  of  the  various 
wave  lengths  of  the  spectrum  upon  the  violet  nerve  would 
give  us  still  another  curve,  as  shown  in  Fig.  394. 

When  a  ray  of  light 
v  falls  upon  the  retina, 
we  may  suppose  these 
three  nerves  to  send 
messages  simultaneously 
to  the  brain,  where  they 
-^  are  combined  in  pro- 
portion to  the  intensity 
of  the  effects  produced.  This  combination  gives  us  the 
sensation  of  color.  Nearly  all  the  phenomena  of  color  are 
satisfactorily  accounted  for  by  the  use  of  this  theory. 


R      0 


FIG.  394. 


388.    EXPERIMENT  123. 

Apparatus  : 


Contrast  Effects. 


(1)  A  sheet  of  red  and  also  a  sheet  of  green  paper.  The  colors  of 
these  should  be  as  nearly  pure  as  it  is  possible  to  obtain  them.1 

1  A  sample  book  of  colored  papers,  which  may  be  procured  from  vari- 
ous manufacturers,  will  be  found  useful  in  the  performance  of  these 
experiments. 


VISION  AND    THE  SENSE  OF  COLOR  423 

(2)  A  small  piece  of  red  paper  differing  slightly  from  the  fore- 
going in  color.  A  corresponding  piece  of  green  paper  also  differing 
slightly  from  the  larger  sheet.  These  pieces  should  be  about  5  cm.  x 
10  cm. 

Procedure  : 

(a)  Cut  the  small  pieces  of  colored  paper  in  half,  making  two 
squares  of  each,  5  cm.  in  diameter. 

(i)  Place  one  of  the  red  squares  upon  the  red  sheet,  and  the  other 
upon  the  green.  Note  that  the  latter  immediately  takes  on  a  much 
livelier  tint  than  the  former,  although  it  has  been  cut  from  the  same 
piece.  This  difference  is  due  to  a  difference  in  the  condition  of  the 
nerves  of  the  eye.  When  we  look  at  the  red  paper  superimposed 
upon  the  background  of  red,  the  red  nerve  of  the  retina  becomes 
fatigued  by  continued  excitation.  The  impression  carried  to  the  brain 
is  therefore  weakened.  When  we  view  the  same  piece  of  paper  upon 
the  green  background,  it  is  the  green  nerve  in  the  eye  which  becomes 
fatigued.  In  both  cases  the  impression  may  be  regarded  as  a  com- 
bination of  the  primary  sensations  of  red  and  green,  because,  as  has 
already  been  stated,  all  wave  lengths  affect  these  two  nerves  to  some 
extent.  When  the  red  nerve  is  fatigued,  the  percentage  of  green  is 
greater  than  the  normal,  and  the  result  is  to  deaden  the  intensity  of 
the  color  effect.  When  the  green  nerve  is  fatigued,  the  relative  strength 
of  this  impression  is  weakened,  and  since  this  is  an  admixture  which 
interferes  with  the  brilliancy  of  the  colors,  the  disappearance  of  it 
heightens  the  impressions  of  red.  These  effects  are  called  contrast 
effects. 

(c)  To  illustrate  this  point  further,  attach  to  one  of  the  small  green 
squares  a  thread  about  50  cm.  in  length.  Place  the  square  upon  the 
red  background,  fixing  the  eye  upon  it  intently,  and  taking  care  not 
to  allow  it  to  wander  for  an  interval  of  about  thirty  seconds ;  then 
withdraw  the  green  square  suddenly  by  means  of  the  thread,  and  do 
not  follow  it  with  the  eye.  It  will  be  found  that  that  portion  of  the 
sheet  of  red  paper  which  had  been  covered  with  the  green  now  appears 
of  a  much  livelier  tint  than  the  surrounding  surfaces.  The  effect 
lasts  for  several  seconds.  It  will  be  found  upon  moving  the  eye  that 
the  brilliant  patch  is  not  a  fixture  upon  the  red  surface,  but  moves  as 
the  eye  moves.  The  explanation  is  as  follows  : 

In  the  small  region  of  the  retina  upon  which  an  image  of  the  green 
patch  had  been  formed,  the  green  nerves  become  greatly  fatigued. 


424  THE  OUTLINES   OF  PHYSICS 

When  the  patch  is  removed,  this  portion  of  the  retina  sends  to  the 
brain  messages  of  red  and  green,  in  which  the  latter  element  is  there- 
fore much  weakened.  The  result  is  a  livelier  impression  of  red  than 
would  be  obtained  were  the  green  nerve  of  its  ordinary  sensitiveness. 

(c?)  Repeat  this  observation,  using  a  red  square  with  thread  at- 
tached, upon  the  green  background.  It  will  be  found  that  the  result 
is  a  greatly  increased  sensitiveness  to  green  in  the  part  of  the  retina 
previously  exposed  to  the  red  square. 

389.  Color  Blindness.  —  Most   people  possess  the  three 
primary  color  sensations,  above  described,  but  about  four 
per  cent  of  the  male  population  lacks  either  the  sensation 
for  red  or  the  sensation  for  green.     Such  people  are  said 
to  be  color  blind,  and  they  are  spoken  of  as  red  blind  or 
green  blind  according  to  the  character  of  the  defect.     This 
peculiarity  of   vision  is  almost  unknown  among  women. 
It  is  an  organic  deficiency  which  cannot  be  overcome  or 
in  any  way  modified   by  training.     Although   the  color 
sense  of  those  individuals  who  have  two  instead  of  three 
primary  colors  is  entirely  different  from  that  of   the  re- 
mainder of  the  race,  they  learn  in  childhood  to  use  the 
same  color  names  as  those  who  have  normal  vision,  and 
oftentimes  they  go  through  life  without  knowing  of  the 
difference  which  exists  between  their  sense  of  color  and 
that  of  their  neighbors.     Color  blindness  can  be  detected 
with  certainty  by  means  of  the  very  simple  method  of  Pro- 
fessor Holmgren  of    Upsala,  Sweden.     This  method  was 
devised  shortly  after  a  terrible  railway  accident  in  that 
country,  which  had  been  caused  by  the  color  blindness  of 
an  employee.     It  is  as  follows : 

390.  The  Holmgren  Test.  —  The  outfit  for  this  test,  which 
may  readily  be  performed  by  any  intelligent  person,  con- 
sists of  a  large  number  of  small  skeins  of  colored  worsted. 
The  colors  are  reds,  greens,  blues,  purples,  and  their  mix- 


.-      VISION  AND   THE  SENSE  OF  COLOR  425 

tures,  together  with  a  variety  of  neutral  grays  and  browns. 
Two  skeins,  one  a  pale  apple  green,  the  other  a  light  reddish 
purple  or  magenta,  are  termed  the  confusion  samples.  The 
person  to  be  tested  is  shown  the  confusion  samples  in  turn, 
and  is  requested  to  select  from  the  other  worsteds  all  those 
which  appear  to  him  most  nearly  related  to  the  former. 

Color-blind  observers  select  worsteds  which  no  one  with 
normal  vision  could  be  brought  to  consider  as  in  any  way 
similar  to  the  confusion  samples.  In  the  selection  made 
by  a  red-blind  subject  we  may  find,  for  example, 

With  the  Apple  Green.  With  the  Magenta. 


(1)  Light  yellows  and  straw 
colors  tending  towards  gray. 

(2)  Pale  pinks. 

(3)  Light    browns     or    fawn 
colors. 


(1)  Purples  and  violets,  both 
light  and  dark  (in  none  of  which 
red  is  predominant). 

(2)  Blues,  both  light  and  dark. 


The  same  observer,  when  requested  to  pick  out  those 
samples  which  resembled  most  nearly  a  skein  of  scarlet 
worsted,  will  include  in  his  selection  all  the  dark  browns 
and  olive  greens. 

The  importance  of  knowing  the  character  of  the  color 
vision  of  those  who  have  to  make  use  of  colored  signals 
is  now  so  well  recognized  that  mariners,  pilots,  soldiers, 
railway  employees,  etc.,  and  in  many  countries  the  whole 
school  population  are  tested  for  color  blindness. 


APPENDIX  I 

TABLE   OF   THE  RELATION  OF  BRITISH  MEASURES 
TO   THE  METRIC   SYSTEM 

(1)  LENGTH. 

The  unit  is  1  centimeter  (cm.)  =  0-393704  inch. 

TV  centimeter    =  1  millimeter  =  0-0393704  inch 

100  centimeters  =  1  meter          =,39-3704  inches 

1000  meters          =  1  kilometer  =  39370-4  inches 

=  1093-6  yards 
=  0-62137  mile 

(2)  AREA. 

The  unit  is  1  sq.  centimeter  (crnT2)  =  0-155000  sq.  inch. 

100  sq.  millimeters  =  1  sq.  centimeter  =  0-155000  sq.  inch 
10,000  sq.  centimeters  =  1  sq.  meter          =  1550-00  sq.  inches 

=  1-19599  sq.  yards 

(3)  VOLUME. 

The  unit  is  1  cu.  centimeter  (cmT8)  =  0-06102  cubic  inch. 

1000  cu.  centimeters  =  1  liter  =  0-26417  U.  S.  gallon 

=  0-22008  Imperial  gallon 
1,000,000  cu.  centimeters  =  1  cu.  meter  =  35-314  cu.  feet 

=  1-3079  cu.  yard 

(4)  MASS. 

The  unit  is  1  gram  =  15-432  grains  =  0-03215  oz.  (Troy) 

=  0-03527  oz.  (Avoirdupois) 
TuVo  gram    =  1  milligram  =  0-015432  grain 
1000  grams  =  1  kilogram    =  2-2046  pounds  (Avoirdupois) 
427 


428  THE  OUTLINES   OF  PHYSICS 

These  tables  give  only  the  metric  values  which  are  used  in  physical 
measurements.  In  the  complete  series  of  quantities  of  the  metric 
system,  parts  and  multiples  of  each  fundamental  unit  are  given  names 
by  means  of  the  prefixes,  milli-  (T^)i  centi-  (T£o)>  deci-  (TO)>  deca- 
(10),  hecto-  (100),  kilo-  (1000),  myria  (10,000). 


APPENDIX   II 

THE  USE  OF   CROSS-SECTION  PAPER 

The  results  of  very  many  physical  measurements  are  capable  of 
being  expressed  graphically  by  means  of  a  curve.  Such  curves  show 
the  relation  between  two  quantities,  which  it  has  been  the  object  of 
the  measurement  to  compare,  in  a  much  more  definite  manner  than 
can  be  done  by  means  of  tables.  One  readily  acquires  the  power  of 
interpreting  such  curves. 

There  are  many  systems  of  co-ordination  by  means  of  which  curves 
can  be  plotted,  but  the  simplest  and  most  useful  of  them  all  is  the 
system  of  rectilinear  or  Cartesian  co-ordinates.  The  paper  used  for 
the  plotting  of  curves  with  Cartesian  co-ordinates  is  divided  into  equal 
squares.  It  is  a  matter  of  convenience  to  have  the  fifth  and  tenth 
lines  heavier  than  the  intervening  .ones.  The  distance  between  lines 
should  be  large  enough  so  that  the  position  of  a  point  anywhere  upon 
the  paper,  with  reference  to  the  intervening  lines  and  to  the  nearest 
heavy  lines,  can  be  seen  at  a  glance  without  straining  the  eyes.  It 
should,  indeed,  be  possible  to  estimate  a  tenth  of  the  smallest  divi- 
sions with  ease. 

The  smallest  squares  which  can  be  readily  used  with  the  naked  eye 
are  square  millimeters.  There  is  a  certain  convenience  in  having  the 
paper  divided  by  lines  the  distances  of  which  are  in  accordance  with 
the  metric  system,  but  for  many  purposes,  especially  where  the  results 
obtained  are  not  accurate  to  more  than  two  places  of  decimals,  a  paper 
with  larger  squares  is  to  be  preferred.  Half  centimeters  would  not 
be  too  coarse  a  division  for  many  purposes. 

It  is  of  much  more  importance  that  the  lines  shall  be  sharply 
defined,  strictly  parallel,  and  precisely  at  right  angles  to  one  another 
than  it  is  to  have  the  squares  of  a  given  size.  Paper  ruled  at  right 


APPENDIX  429 

angles  by  means  of  ordinary  ruling  pens  is  not  sufficiently  accurate. 
To  be  satisfactory,  it  must  be  printed  from  an  engraved  plate.  Such 
plates  are  quite  expensive,  and  it  is  therefore  not  feasible  to  get  paper 
of  any  desired  size.  One  has  to  choose  between  those  which  are 


FIG.  395. 


already  on  the  market.  Figure  395  shows  a  portion  of  a  sheet  of  cross- 
section  paper,  the  squares  of  which  are  large  and  open.  Such  paper 
is  well  adapted  for  the  plotting  of  many  of  the  curves  obtained  in  the 
experiments  described  in  this  book. 


APPENDIX   III 

BALANCES   AND  WEIGHTS 

The  measurement  of  mass  is  one  of  the  chief  occupations  of  the 
experimenter  in  physics,  and  a  laboratory,  however  simple  in  its 
equipment,  must  therefore  be  provided  with  balances  and  weights. 
Every  laboratory  should  contain  at  least  two  balances ;  one  for  the 
weighing  of  considerable  masses,  namely,  from  5  to  500  g.,  and  a 
finer  balance  for  the  weighing  of  masses  less  than  100  g.  The  latter 


430  THE  OUTLINES  OF  PHYSICS 

should  be  a  simple  form  of  analytical  balance  such  as  is  used  in 
chemistry.  It  is  well  to  place  the  very  finest  grade  of  such  instru- 
ments in  the  hands  of  beginners.  Both  balances  should  be  of  good 
construction  in  their  essential  features  and  both  should  be  provided 
with  a  pointer  and  scale.  It  is  desirable  that  the  fine  balance  should 
be  inclosed  in  a  glass  case  to  obviate  the  disturbances  from  blasts  of 
air.  The  balance  for  heavy  masses  should  have  broad  pans  and  a 
stiff  beam. 

Should  an  analytical  balance  prove  too  expensive,  for  the  finer 
weighings,  a  substitute  may  be  provided  by  purchasing  a  portable 
hand  balance  with  pans,  and  mounting  the  same  upon  a  homemade 
wooden  stand.  This  balance  can  be  purchased  for  a  small  sum  of 
any  uealer  in  chemical  supplies.  It  is  a  useful  instrument,  but  should 
be  used  as  an  accessory  to  the  better  form  and  not  as  a  substitute 
for  it,  if  it  be  possible  to  obtain  the  latter. 

There  should  be  at  least  two  sets  of  brass  weights,  the  first  running 
from  1  kg.  to  1  g.  for  use  with  the  heavy  balance,  the  second  from 
100  g.  to  1  mg.  for  finer  weighings.  It  will  be  found  advantageous 
likewise  to  have  on  hand  a  considerable  number  of  extra  weights 
below  1  g.,  since  these  on  account  of  their  small  size  are  easily  lost. 
For  all  ordinary  practice  work,  what  are  technically  called  second- 
quality  weights  are  sufficiently  accurate.  They  cost  much  less  than  the 
weights  of  the  first  quality ;  upon  the  final  adjustment  of  which  much 
labor  has  to  be  expended.  A  set  of  the  latter  is  valuable  in  any 
laboratory  as  a  reference  standard  by  means  of  which  the  accuracy  of 
the  second-quality  weights  may  be  tested.  They  should  be  reserved 

for  such  purposes,   and  not  put  into 
general  use. 

In  addition  to  these  weights,  the  lab- 
oratory should  be  furnished  with  a  large 
number  of  iron  weights.  These  cannot 
be  found  in  the  stock  of  dealers  in 
scientific  apparatus,  but  they  may  be 
obtained  to  order  at  any  iron  foundry. 
It  is  convenient  to  have  three  sizes,  5  kg., 
1  kg.,  and  T^  kg.  Of  each  size  there  are 
FIG.  396.  two  Distinct  forms.  One  is  a  disk  of 

cast  iron  into  which  an  iron  rod  bent  into  a  hook  at  one  end  and 
flattened  at  the  other  is  inserted,  as  shown  in  Fig.  396.  The  other 


APPENDIX  431 

form  is  a  disk  with  a  slot  extending  in  past  the  center,  of  a  sufficient 
width  to  enable  the  weight  to  slip  over  the  weight  to  which  the  hook 
is  attached.  These  two  forms  should  be  provided  in  all  the  sizes  just 
mentioned.  If  patterns  be  provided  in  the  following  dimensions,  the 
castings  will  be  very  nearly  of  the  proper  weight. 

DIMENSIONS  OF  PATTERNS  FOR  WEIGHTS. 

f  Diameter  16-2  cm. 

5  kilograms  j  Thickness  3-6  cm. 

I  Width  of  slot     1-2  cm. 

f  Diameter  10-0  cm. 

1  kilogram  |  Thickness  1-9  cm. 

I  Width  of  slot     1-3  cm. 

(  Diameter  4-4  cm. 

JQ  kilogram  |  Thickness  0-9  cm. 

I  Width  of  slot     0-7  cm. 

For  the  hooks  (1  and  5  kg.)  iron  rods  1  cm.  (f")  in  diameter  and 
26  crn.  long  may  be  used.  The  disks  are  cast  without  slots  and  about 
0-4  cm.  thinner  than  the  slotted  weights.  For  the  TV  kg.  hook  weights, 
rods  0-5  cm.  (TV)  and  26  cm.  long  may  be  used.  The  disks  need  be 
only  O4  cm.  in  thickness. 

Cast-iron  weights  of  the  forms  just  described  are  not  sufficiently 
accurate  just  as  they  come  from  the  foundry,  even  for  ordinary  prac- 
tice experiments.  They  should  therefore  be  adjusted.  If  the  pat- 
terns are  of  the  sizes  just  described,  the  weights  will  nearly  all  be 
slightly  in  excess  of  the  desired  value.  Only  such  castings  as  contain 
openings  and  blow  holes  of  considerable  size  will  fall  below  the  nor- 
mal weight.  The  weights  should  be  taken  in  turn  and  placed  upon 
the  pan  of  the  large  balance.  It  having  been  found  by  about  how 
much  they  are  in  excess,  a  hole  or  a  set  of  shallow  holes  may  be 
drilled  in  the  lower  side.  When  a  lathe  is  not  available,  it  is  necessary 
to  have  the  adjustment  made  in  a  machine  shop. 

The  hook  weights,  of  which  there  should  be  one  for  every  ten  of 
the  slotted  weights,  are  most  readily  adjusted  by  cutting  off  the  end 
of  the  iron  rod  before  bending  the  same.  The  size  of  the  disk  given 
for  such  weights  in  the  preceding  table  is  such  as  to  allow  for  rods  of 
the  length  indicated  in  the  table.  After  adjustment  the  weights 
should  be  painted  with  asphalt  varnish. 


432 


THE  OUTLINES   OF  PHYSICS 


APPENDIX   IV 

READING   MICROSCOPES 

For  the  measurement  of  very  small  distances  the  instrument  em- 
ployed is  the  reading  microscope.  Measurements  with  this  instru- 
ment are  made  in  one  of  the  following  three  ways : 

1.  Method  of  the  Eyepiece  Scale.  —  The  eyepiece  scale  is  the  simplest 
attachment  by  means  of  which  micrometric  measurements  can  be 
made.  It  consists  of  a  set  of  lines  ruled  upon  a  glass  slide.  This  is 
slipped  into  the  eyepiece  of  the  microscope  through  openings  cut 
opposite  to  one  another  in  the  tube.  These  openings  are  so  situated 
that  the  scale  upon  the  glass  will  be  precisely  in  the  focus  of  the  eye- 
piece. The  real  image  formed  by  the  objective  will  then  be  seen 
superimposed  upon  this  glass  scale,  and  its  dimensions  can  be  read  in 


FIG.  397. 


FIG.  398. 


terms  of  the  scale  divisions.  For  eyepieces  of  ordinary  power,  the 
lines  of  the  glass  scale  should  be  one  one-hundredth  of  a  centimeter 
apart.  It  is  customary  to  rule  fifty  such  lines  upon  the  eyepiece  scale. 
In  order  to  reduce  the  reading  obtained  by  means  of  this  device  to  cen- 
timeters, it  is  necessary  to  calibrate  the  eyepiece  scale  by  observations 
upon  some  object  of  known  size  placed  under  the  microscope.  This 
object  may  be  another  scale  ruled  upon  glass  or  metal,  or  where  that 
is  not  available,  a  fair  degree  of  accuracy  may  be  obtained  by  placing 
in  the  field  of  the  microscope  some  object,  such  as  a  wire,  the  diameter 
of  which  has  been  carefully  determined  with  a  micrometer  gauge. 
The  diameter  of  this  object  is  observed  in  scale  divisions,  and  the 
value  of  one  scale  division  in  centimeters  is  computed  from  the  obser- 
vation. Figure  397  shows  an  eyepiece  provided  with  an  ordinary 


APPENDIX 


433 


micrometer  scale,  and  Fig.  398  the  appearance  of  the  scale  as  it  is 
seen  through  the  eye  lens. 

2.  Method  of  the  Eyepiece  Micrometer.  — The  eyepiece  micrometer 
is  a  device  by  means  of  which  a  cross  hair  in  the  focus  of  an  eye- 
piece is  moved  across  the  field  of 
view  by  turning  a  micrometer 
screw.  The  position  of  the  cross 
hair  is  read  by  means  of  a  scale 
upon  the  periphery  of  a  drum- 
shaped  head  attached  to  the  screw. 
Figure  399  shows  a  microscope 
provided  with  the  usual  form  of 
an  eyepiece  micrometer.  There  is 


FIG.  39R 

commonly  a  fixed  cross  hair  to  mark 
the  middle  of  the  field  of  view,  and 
sometimes  the  moving  hair  is  sup- 
planted by  two  crossing  each  other  at 
an  oblique  angle.  In  the  latter 


FIG.  401. 


FIG.  400. 


case  the  appearance  of  the  field  is  that  represented  in  Fig.  400. 

This  is  a  more  elaborate  device  than  the  eyepiece  scale,  and  admits 
2r 


434 


THE  OUTLINES  OF  PHYSICS 


of  greater  accuracy  of  observation.  Like  the  former,  however,  it  must 
be  calibrated  by  reference  to  a  scale  or  an  object  of  known  size  placed 
under  the  microscope. 

3.  Method  of  the  Micrometer  Stage.  — In  this  method  the  micrometer 
screw  is  attached  to  the  stage  of  the  microscope,  and  the  object  is 
moved  through  the  field  of  view  by  turning  the  screw.  There  is  in 
the  eyepiece  a  fixed  cross  hair.  This  method  has  one  advantage  over 
the  foregoing,  namely,  that  it  is  the  movement  of  the  object  itself 
which  is  measured.  The  pitch  of  the  screw  being  known,  there- 
fore, it  is  not  necessary  to  calibrate  the  instrument.  Sometimes  the 
micrometer  screw  is  so  arranged  as  to  move  the  body  of  the  micro- 
scope across  a  fixed  stage.  Figure  401  shows  a  microscope  provided 
with  the  latter  adjustment. 


APPENDIX  V 

FILTERING  PUMPS 

The  filtering  pump,  or  aspirator,  was  originally  designed  for  the 
production  of  the  partial  vacuum  employed  by  chemists  to  hasten 
the  process  of  filtering ;  it  is,  however,  a 
very  useful  instrument  in  the  physical 
laboratory.  The  principle  of  these  pumps 
may  be  seen  from  a  consideration  of 
Fig.  402.  AB  in  this  figure  is  a  metal 
tube  attached  to  the  water  faucet.  This 
is  contracted  to  narrow  aperture,  and 
opposite  the  contraction  a  horizontal  tube, 
CD,  also  of  small  bore,  enters.  Upon 
opening  the  faucet,  the  stream  of  water 
flows  through  the  vertical  tube.  If  the 
pressure  be  considerable,  this  is  broken 
in  falling,  and  upon  passing  the  opening 
of  the  horizontal  tube,  it  entraps  air 
which  it  carries  down  with  it  and  dis- 
charges below.  If  the  horizontal  tube  be  attached  to  a  closed  receiver, 
the  air  from  this  receiver  will  be  rapidly  removed  by  the  process  just 
described,  and  a  partial  vacuum  will  be  formed. 


FIG.  402. 


APPENDIX 

=^-:~-._ 


435 


It  is  possible  to  make  an  aspirator  out  of  metal  or  even  glass  after 
a  few  trials,  which  will  work  fairly  well.  The  precise  relation  between 
the  parts  is,  however,  an  essential  matter,  and  it  is  better  to  buy  the 
instrument,  which  may  be  had  at  a  low  price  from  any  dealer  in 
chemical  apparatus.  The  best  forms  of  aspirator  are  capable  of 
maintaining  a  vacuum  corresponding  to  a  pressure  of  less  than  5  cm. 
of  mercury. 


APPENDIX  VI 


•THE  CONSTRUCTION  OF  A  SENSITIVE  GALVANOMETER 

It  is  possible  by  paying  attention  to  the  essential  parts  of  the 
instrument  to  construct  a  galvanometer  which,  although  seemingly 
rude,  will  be  sufficiently  sensitive  not 
only  to  perform  the  various  experi- 
ments described  in  this  book,  but  for 
work  of  much  greater  delicacy.  Such 
an  instrument,  made  in  the  very  sim- 
plest manner,  is  shown  in  Fig.  403. 

To  construct  it  take  a  pine  block 
5  cm.  x  10  cm.  x  20  cm.  From  the 
same  material  cut  out  a  wooden  base 
20  cm.  square  and  5  cm.  in  thickness. 
For  the  coils,  of  which  in  the  form 
of  instrument  under  consideration 
there  are  two,  one  above  the  other, 
take  silk-covered  copper  wire.  The 
size  of  the  wire  will  depend  upon 

the  uses  to  which  the  galvanometer  is  to  be  put.  For  the  experiments 
described  in  this  book  rather  coarse  wire  should  be  selected,  namely, 
No.  20  to  24. 

To  wind  the  coils,  take  a  large  empty  spool,  of  the  kind  used  for  the 
coarser  varieties  of  linen  thread.  From  some  thick  sheet  brass  or 
copper,  cut  out  a  disk  corresponding  in  size  to  the  head  of  the  spool, 
namely,  about  4  cm.  in  diameter,  and  to  the  center  of  this  disk 
solder  a  brass  rod,  which  must  be  small  enough  to  pass  freely 


FIG.  403. 


436  THE  OUTLINES  OF  PHYSICS 

through  the  hole  in  the   spool.     This  rod  should  be  about  10  cm. 

long.      Saw  the   spool  in  two  transversely  at  a  distance  of  3  cm. 

from  one  end.  Insert  the  brass  rod  through  the  hole  in  that 

part  of  the  spool  which  has  the  longest 
shank,  as  shown  in  Fig.  404,  and  having 
drawn  it  snugly  up  into  place,  clamp  it 
there  by  means  of  a  hand  vise.  The 
result  of  this  combination  is  a  reel  upon 
which  the  coil  is  to  be  wound.  One  head 


FlG  ^  of  this  reel  is  the  metal  disk,  the  other 

the  wooden  head  of  the  spool.  Wind 

the  reel  full  of  the  wire  selected  for  the  galvanometer,  bringing  both 
ends  over  the  edge  of  the  spool  head. 

Dip  the  coil,  reel  and  all,  into  a  bath  of  melted  paraffin,  and  allow 
the  liquid  to  work  its  way  well  into  the  spaces  between  the  wires. 
After  cooling,  heat  the  metal  head  of  the  reel  carefully  until  it  is 
possible  to  detach  it  from  the  coil  of  wire.  We  now  have  the  coil 
still  mounted  upon  the  spool  with  one  flat  face  exposed.  Make  a 
second  precisely  similar  coil,  using  for  the  purpose  another  empty 
spool.  These  coils  are  to  be  mounted  in  the  block  of  wood  described 
in  the  first  paragraph  of  this  appendix.  With  an  adjustable  auger 
bore  two  holes  through  the  block  with  a  diameter  just  sufficient  to 
admit  the  heads  of  the  spools.  The  distance  between  the  centers  of 
these  holes  should  be  about  6  cm.  Insert  the  coils  into  these  holes, 
pushing  them  through  until  the  exposed  faces  left  by  the  removal  of 
the  metal  disk  are  flush  with  one  face  of  the  block,  and  cement  them 
into  that  position  by  the  application  of  paraffin.  The  four  terminal 
wires  from  these  coils  are  to  be  brought  out  to  the  back  of  the  block 
and  fastened.  The  block  is  then  mounted  in  an  upright  position 
upon  the  center  of  the  wooden  base  and  is  fastened  by  means  of  two 
brass  screws  from  below.  To  the  front  edges  of  the  block  attach 
strips  of  wood,  grooved  so  as  to  admit  a  window  of  plate  glass  as 
shown  in  Fig.  403.  This  window  is  so  placed  as  to  leave  a  clear 
space  of  1  cm.  between  the  block  and  the  glass. 

It  now  remains  to  provide  a  suitable  suspension  for  the  galvanome- 
ter. For  this  purpose  remove  one  of  the  thin  bamboo  splints  from  an 
ordinary  Japanese  paper  fan  and  cut  from  it  a  strip  about  10  cm. 
long.  At  points  equidistant  from  the  two  ends  of  this  strip  mark 
transverse  lines.  The  distance  between  these  lines  must  equal  that 


APPENDIX 


437 


I  P,BE 


between  the  centers  of  the  two  coils  of  wire  in  the  block.  These 
marks  indicate  the  positions  of  the  needles.  The  needles  may  be 
constructed  of  bits  of  steel,  cut  from  a  watch  spring, 
about  6  cm.  in  length.  The  two  pieces  should  be  as 
nearly  as  possible  of  the  same  size,  and  they  should 
be  cut  from  the  same  strip  of  metal.  They  may  be 
magnetized  simultaneously ;  either  by  placing  them  in 
the  axis  of  a  coil  of  wire  through  which  a  strong  current 
is  flowing,  or  between  the  poles  of  an  electromagnet. 
After  magnetization  they  are  to  be  mounted  upon  the 
bamboo  strip  over  the  lines  already  drawn.  The  north- 
pointing  pole  of  one  must  correspond  in  position  to  the 
south-pointing  pole  of  the  other,  as  indicated  in  Fig.  405. 
Midway  between  the  needles  the  mirror  is  to  be  mounted. 
The  simplest  plan  is  to  purchase  a  plane  galvanometer 
mirror,  1  cm.  in  diameter.  It  is  possible  to  make  good 
mirrors  by  silvering  a  considerable  number  of  microscope 
cover  glasses  by  the  method  described  in  Kohlrausch's 
Physical  Measurements.  Unless  one  desires  to  make  a 
considerable  number  of  mirrors,  however,  it  is  better  to 
purchase  them  of  a  dealer  in  physical  apparatus. 

The  bamboo  strip  is  to  be  suspended  by  means  of  a 
fiber  of  unspun  silk  from  a  cocoon.  One  end  of  this  is  attached  to 
the  middle  of  one  end  of  the  strip  by  means  of  a  drop  of  shellac. 
The  free  end  is  then  passed  up  through  a  hole  in  a  strip  of  sheet 
zinc  and  is  fastened  to  the  top  of  the  block.  The  height  must  be 
such  as  to  bring  the  needles  opposite  the  centers  of  the  two  coils. 
A  bit  of  beeswax  will  suffice  to  fasten  the  fiber. 
The  zinc  strip  may  be  given  the  form  shown 
in  Fig.  403,  or  it  may,  preferably,  be  bent  up- 
ward into  a  sort  of  goose  neck  and  then  down 
as  in  Fig.  406.  In  this  form  it  is  readily  adjust- 
able and  the  suspension  can  be  brought  closer  to  the  face  of  the 
block  or  moved  from  the  same  by  the  use  of  the  pliers.  In  setting 
up  the  galvanometer  the  suspension  should  be  brought  as  close  to  the 
face  of  the  block  as  it  can  without  striking.  It  may  be  found  neces- 
sary to  protect  the  suspension  from  draughts  by  filling  in  the  opening 
at  the  top  of  the  plate  glass  window  with  a  layer  of  cotton  batting. 
To  set  up  the  instrument  thus  constructed,  three  wooden  wedges 


FIG.  405. 


FIG.  406. 


438  THE  OUTLINES   OF  PHYSICS 

may  be  made  to  take  the  place  of  leveling  screws.  The  galvanometer 
must  be  placed  upon  a  firm  support  free  from  tremor  and  at  a  dis- 
tance from  large  masses  of  iron,  such  as  iron  columns  and  girders 
and  from  iron  steam  pipes,  etc.  It  should  be  turned  with  the  axis  of 
its  coils  approximately  perpendicular  to  the  magnetic  meridian  and 
should  be  left  so  that  the  suspended  parts  swing  freely. 

To  adjust  the  direction  in  which  the  astatic  pair  of  magnets  are  to 
place  themselves,  a  controlling  magnet  consisting  of  an  ordinary  bar 
magnet  should  be  provided.  This  is  to  be  laid  upon  the  table  or 
shelf  where  the  galvanometer  is  mounted  or  upon  any  convenient 
stand  in  the  neighborhood,  and  it  must  be  shifted  until  the  galva- 
nometer needles  come  into  the  desired  position.  By  placing  this 
magnet  so  that  its  lines  of  force  oppose  the  field  of  the  earth,  the 
sensitiveness  of  the  instrument  can  be  increased.  By  placing  it  with 
its  lines  of  force  parallel  to  the  field,  the  sensitiveness  of  the  galva- 
nometer will  be  reduced. 

The  Reading  Telescope. — In  order  to  make  measurements  with  a 
galvanometer  like  that  just  described,  it  is  necessary  to  have  a  read- 
ing telescope.  The  simplest  and  one  of  the  best  forms  for  this  pur- 
pose consists  of  an  ordinary  spyglass,  which  may  be  purchased  of 
any  optician  for  a  small  sum.  The  objective  of  this  spyglass  should 
be  at  least  3  cm.  in  diameter.  The  draw  tube  of  such  telescopes 
is  not  long  enough  to  admit  of  focusing  them  upon  objects  near 
at  hand ;  but  by  unscrewing  them  at  the  joint  nearest  the  eyepiece 
and  removing  the  "  erecting  lens,"  the  instrument  is  readily  adapted 

to  use  as  a  reading  telescope.  The 
image  which  it  now  produces  is 
inverted,  but  it  comes  to  a  focus 
much  nearer  the  objective  and 
within  the  range  of  the  draw  tube. 
The  spyglass  thus  converted  into 
a  reading  telescope  should  be 

FIG  407  mounted  on   a  wooden  stand  of 

the  form  shown  in  Fig.  407.     A 

paper  scale  at  least  50  cm.  long,  and  divided  either  into  millimeters 
or  tenths  of  inches,  and  mounted  upon  a  wooden  strip,  is  set  up  in  a 
horizontal  position  just  below  the  telescope.  The  reading  telescope 
with  its  scale  should  be  set  up  at  a  distance  of  1  or  2  m.  from  the 
galvanometer.  The  telescope  should  be  focused  upon  objects  at  twice 


APPENDIX  439 

that  distance.  If,  then,  it  be  pointed  at  the  mirror  from  a  position 
such  that  the  image  of  the  scale  can  be  seen,  the  divisions  upon  the 
latter  will  be  nearly  in  focus. 

The  construction  of  such  a  homemade  galvanometer  is  a  matter 
requiring  some  little  skill  and  patience,  and  the  mastery  of  the  in- 
strument after  it  has  been  constructed  is  likewise  somewhat  difficult. 
To  the  student  of  physics,  however,  there  is  no  instrument  more 
important,  and  the  time  required  to  learn  its  construction  and  to  gain 
command  of  it  is  well  employed.  In  a  laboratory  containing  a  con- 
siderable number  of  students,  it  is  wise  to  provide  several  instruments 
of  the  type  described  above.  In  such  a  case  the  services  of  a  carpenter 
will  enable  the  teacher  to  secure  a  valuable  equipment  at  very  small 
expense. 


APPENDIX   VII 

A   SIMPLE   FORM   OF   GLASS   CELL 

To  make  a  glass  cell  with  plane  sides  suitable  for  use  in  the  field 
of  the  lantern,  take  two  pieces  of  plate  glass  about  15  cm.  square. 
Bend  a  piece  of  glass  tubing  into  the  shape 
shown  in  Fig.  408.  Over  this  bent  tube, 
when  cool,  slip  a  rubber  tube  which  should 
fit  it  rather  snugly.  The  bent  tube  with  its 
rubber  coating  may  now  be  laid  between 
the  glass  plates,  and  they  may  be  pressed 
against  it  so  that  the  rubber  will  make  con- 
tact with  the  glass  at  every  point.  A  water-  -pIG 
tight  cell  is  thus  produced.  The  walls  of 

the  cell  may  be  held  in  place  by  means  of  simple  clamps  of  the 
form  commonly  used  in  such  cells,  or  they  may  be  tied  temporarily 
by  means  of  a  strong  cord,  and  the  outer  space  between  the  tube 
and  the  glass  plates  may  be  filled  in  with  beeswax  or  rosin,  or  other 
suitable  cement.  The  cord  may  then  be  cut  away,  and  the  cell  will 
retain  its  form. 


440  THE   OUTLINES   OF  PHYSICS 

APPENDIX   VIII 

THE  CONSTRUCTION  OF  AN  ELECTROSCOPE 

To  make  a  serviceable  electroscope,  cut  out  a  disk,  about  4  cm.  in 
diameter,  of  sheet  metal  (copper,  brass,  or  zinc).  The  metal  should 
be  1  or  2  mm.  in  thickness.  Round  off  the  edges  of 
the  disk  with  a  file,  and  solder  to  its  center  a  piece  of 
copper  wire  about  10  cm.  long.  Over  the  wire  slip  a 
piece  of  glass  tubing  5  cm.  long,  and  seal  the  glass  in 
place  at  the  middle  of  the  wire  by  means  of  melted 
sulphur,  resin,  or  paraffin.  With  a  pair  of  pliers  bend 
the  free  end  of  the  wire  into  the  form  shown  in  Fig. 
409,  adjusting  carefully  so  that  the  horizontal  portion 
will  be  straight  and  exactly  parallel  to  the  plane  of 
the  disk. 

Select  a  round,  short-necked  bottle  of  white  glass.  It 
should  be  8  to  10  cm.  in  diameter,  and  must  have  a 
neck  wide  enough  to  admit  the  glass  tube  freely.  Fit 
the  tube  to  the  bottle  by  means  of  a  cork,  a  rubber 
stopper,  or  a  collar  made  of  rubber  tubing.  Cut  from  a  sheet  of  gold 
leaf  a  strip  about  8  cm.  long  and  0-5  cm.  in  width.  This  is  readily 
done  with  a  pair  of  scissors  or  a  very  sharp  knife,  by  allowing  the 
sheet  of  gold  to  remain  between  the  adjacent  leaves  of  the  "book" 
and  cutting  through  the  leaves  and  through  the  layer  of  gold  which 
they  inclose,  at  a  single  stroke. 

The  mounting  of  the  leaves  must  be  performed  in  a  place  free  from 
draughts.  It  is  an  operation  of  considerable  delicacy,  the  success  of 
which  depends  upon  the  following  points:  The  gold  leaf  is  to  be 
handled  only  with  dry  metal  tools.  To  any  wet  surface  the  leaf  will 
cling,  and  cannot  be  detached  without  tearing.  Dry  non-metallic 
tools  become  electrified,  and  attract  the  foil  with  a  similar  result. 

By  means  of  a  joiner's  clamp  mount  a  clean  dry  steel  knitting 
needle  horizontally  as  in  Fig.  410.  With  one  blade  of  the  scissors, 
or  with  a  knife  blade,  carefully  remove  the  upper  layer  of  paper  from 
the  strip  of  gold  leaf,  and  the  latter  from  the  underlying  paper. 
The  tendency  of  the  gold  and  paper  to  adhere  at  the  cut  edges  consti- 
tutes the  chief  difficulty  of  the  entire  operation  and  makes  it  neces- 
sary, sometimes,  to  cut  several  strips  before  one  can  be  detached  entire. 


APPENDIX 


441 


The  strip  is  to  be  raised  upon  the  tool  and  laid  over  the  knitting 
needle.  It  is  to  be  adjusted  until  the  ends  hang  down  vertically 
and  to  the  same  length,  side  by  side  from  the  needle,  which  will  then 
support  the  strip,  folded  transversely  at  its 
middle.  (See  Fig.  410.) 

The  horizontal  arm  of  the  wire  shown  in 
Fig.  409  is  then  to  be  touched  along  its 
lower  face  with  shellac  or  other  varnish, 
after  which  it  is  to  be  brought  down  care- 


FIG.  410. 


FIG.  411. 


fully  from  above  until  it  makes  contact  with  the  strip  of  gold  leaf  at 
the  fold.  The  latter  will  cling  to  the  wire  and  may  then  be  trans- 
ferred to  the  bottle.  The  electroscope  thus  constructed  will  be 
similar  to  that  depicted  in  Fig.  176. 

A  form  of  electroscope  more  suitable  for  use  in  the  field  of  the 
lantern  is  shown  in  Fig.  411. 

The  gold  leaves  hang  in  the  middle  of  a  horizontal  cylindrical 
brass  box,  15  cm.  in  diameter,  with  glass  ends.  The  beam  of  light 
from  the  lantern  passes  through  the  parallel  glass  plates,  which  form 
the  ends  of  this  inclosing  vessel,  without  appreciable  distortion,  and 
a  good  image  of  the  gold  leaves  is  projected  upon  the  screen. 


APPENDIX   IX 


THE   USE   OF   THE   LANTERN 


No  instrument  is  more  useful  in  the  physical  laboratory  than  a 
suitable  lantern  for  projection.      It   is   important  that   the   lantern 


442 


THE  OUTLINES   OF  PHYSICS 


FIG.  412. 


should  be  so  constructed  as  to  allow  free  space  between  the  condens- 
ing lens  and  the  objective,  so  that  apparatus  of  various  kinds  may  be 
readily  inserted.  Many  lanterns  are  intended  for  use  with  lantern 

slides  only.  Next  of  importance  in 
the  selection  of  the  lantern  is  the 
question  of  the  source  of  light  to  be 
employed.  The  most  powerful  light 
is  that  of  the  electric  arc,  and  this 
should  be  used  whenever  practicable. 
To  produce  a  satisfactory  effect,  the 
carbons  of  the  arc  lamp  must  be  so 
inclined  as  to  bring  the  crater  of  the 
positive  carbon  into  view  from  the  cen- 
ter of  the  condensing  lens.  (See  Fig. 
412.)  It  is  furthermore  important 
to  use  carbons  of  the  very  best  quality. 
The  incessant  flickering  and  the  hissing  of  most  arc  lights  are  due  to 
the  poor  quality  of  the  carbon  pencils.  Arc  lamps  are  to  be  had 
which  are  constructed  especially  for  use  in  the  lantern,  and  these  may 
be  employed  wherever  a  direct-current  incandescent  lighting  circuit  is 
at  command.  Since  the  potential  difference  necessary  to  maintain 
the  arc  is  only  about  50  volts,  it  is  necessary  to  place  a  considerable 
resistance  in  series  with  the  lamp  on  such  a  circuit.  Resistance  boxes 
(rheostats)  specially  designed 
for  this  purpose  are  easily  ob- 
tained, or  one  may  be  construct- 
ed which  will  answer  every 
purpose,  by  taking  four  full- 
sized  sheets  of  tinned  iron  and 
slitting  them  nearly  through 
from  opposite  sides  at  distances 
of  about  1  cm.  with  tinmen's 
shears.  The  method  of  cutting 
is  shown  in  Fig.  413.  These  may  be  mounted  upon  a  wooden  frame 
as  shown  in  Fig.  414,  and  their  adjacent  free  ends  may  be  attached 
together.  We  thus  have  a  long  strip  of  thin  sheet  metal  capable 
of  carrying  15  or  20  amperes  of  current  without  undue  heating.  The 
apparatus  is  cheap,  serviceable,  and  easily  portable.  In  laboratories 
where  electrical  work  is  going  on  such  resistance  frames  are  very  use- 


FIG.  413. 


APPENDIX  443 

fill.  One  such  frame  placed  in  series  with  the  arc  lamp  is  more  than 
sufficient  to  reduce  the  current  to  the  suitable  size. 

Where  the  arc  lamp  is  not  available,  the  source  of  light  usually 
employed  is  the  lime  light.  This  is  an  expensive  and  inconvenient 
light ;  involving  as  it  does  the  manufacture  of  oxygen,  or  the  purchase 
of  oxygen  and  hydrogen  in  iron  cylinders. 

It  seems  likely  that  the  acetylene  flame  will  entirely  supplant  the 
lime  light  for  use  in  the  lantern.  The  illumination  attained  from  a 
suitable  acetylene  burner  is  fully  equal,  both  as  regards  brightness 


FIG.  414. 

and  color,  to  that  of  the  lime  light.  Generators  are  obtainable  of  the 
manufacturers  of  lanterns  by  means  of  which  the  acetylene  gas  can  be 
produced  directly  from  calcium  carbide  at  a  sufficient  rate  to  supply 
the  burner.  Care  should  be  exercised,  as  in  the  case  of  all  illuminat- 
ing gases,  to  avoid  explosions  by  mixture  with  air.  Experiment  has 
shown  that  acetylene  is  particularly  dangerous  when  stored  at  con- 
siderable pressures.  When  generated  freely,  as  fast  as  it  is  used,  there 
should  be  no  serious  danger.  Teachers  using  the  lantern  will  find 
much  that  is  suggestive  and  valuable  in  the  following  books:  Lewis 
Wright  on  Light;  Dolbear,  On  the  Art  of  Projecting ;  Hopkins,  Experi- 
mental Science,  Chapter  XXTT. 


INDEX 


Aberration,  chromatic,  398 ; 

spherical,  397. 
Absolute  pitch,  351. 
Absorption  spectra,  380. 
Absorption    spectrum    of    chlorophyl 
and   potassium    permanganate, 
388. 

Acceleration,  28. 
Accommodation,  in  vision,  413. 
Achromatic  lenses,  399. 
Action  of  current  upon  a  magnet,  277. 
Adhesion,  86. 

Air  columns,  vibration  of,  362. 
Air  thermometer,  the,  157. 
Ampere's  rule,  279. 
Analyzer  and  polarizer,  406. 
Angle  of  contact,  134 ; 

of  refraction,  378. 

Angles  of  incidence  and  reflection,  371. 
Aperture  of  lenses,  395. 
Aqueous  humor  of  the  eye,  415. 
Archimedes,  principle  of,  116. 
Arc  light,  the,  305. 
Atmosphere,  nature  of,  141. 
Attraction,  electrostatic,  211. 
Attractive   and    repellent    forces   be- 
tween a  magnet  and  a  wire  car- 
rying current,  325. 
Audibility,  limits  of,  342. 
Axle,  the  wheel  and,  70. 

Balance,  the,  79 ; 

sensitiveness  of,  86. 
Ballistic  curve,  34. 
Barometer,  construction  of,  140. 
Battery,  plunge,  270. 
Beats,  graphic  representation  of,  352 ; 

the  method  of,  351. 


Bells,  345. 

Binocular  vision,  417. 

Boiling   point,  influence  of   pressure 

upon, 178 ; 

and  pressure,  relation  between,  180. 
Bowed  strings,  motion  of,  357. 
Boyle's  law,  137. 
Bridge,  Wheatstone's,  297. 
Bright-line  spectra,  386. 
Brightness  of  image  and  aperture  of 

lens,  394. 
British  units  and  the  metric  system,  3. 

Calorimeter,  the  ice-block,  165. 
Calorimetry,  161. 
Capacity  for  heat,  161. 
Capacity,  of  water,  thermal,  162 ; 

specific  inductive,  246. 
Cell,  bichromic,  269; 

simple,  266 ; 

voltaic,  forms  of,  268. 
Cells,  closed  circuit,  properties  of,  269. 
Centimeter  and  inch  compared,  4; 

defined,  2. 
Charge,  bound  and  free,  250 ; 

distribution  of,  240 ; 

induced,  distribution  of,  243; 

intensity  of,  238. 

Charges,  equal  and  opposite,  222. 
Charging  by  contact,  217 ; 

by  induction,  219. 
Charles's  law,  157. 
Chladni's  figures,  343. 
Chlorophyl,  spectrum  of,  388. 
Chromatic  aberration,  398. 
Circular  plates,  vibration  of,  345. 
Closed  and  open  pipes,  362. 
Closed  circuit  cells,  properties  of,  269. 


445 


446 


INDEX 


Cohesion,  86. 
Coils,  induction,  330. 
Coincidences,  method  of,  42. 
Color,  denned,  417 ; 

by  interference,  409; 

of  pigments,  418 ; 

of  soap  films,  409 ; 

purity  and  saturation  of,  418 ; 

sensations,  theory  of,  420. 
Color  blindness,  424. 
Concave  mirrors,  373. 
Condensers,  245 ; 

capacity  of,  249. 
Conduction,  194. 

Conductivity    (thermal)    of    copper, 
iron,  and  glass,  194 ; 

of  liquids,  196. 

Conductors  and  non-conductors,  221. 
Conjugate  foci,  374; 

of  a  lens,  391. 

Conservation  of  energy,  law  of,  64. 
Contact,  angle  of,  134 ; 

charging  by,  217. 
Continuous  spectra,  386. 
Contrast,  422. 
Convection,  194,  198. 
Converging  lenses,  391. 
Convex  mirrors,  373. 
Copper,  conducting  power  of,  194 ; 

electrolysis  of,  309. 
Copper  voltameter,  measurement   of 

current  by,  312. 
Current,  action  of,  upon  a  magnet,  277 ; 

the  electric,  265 ; 

heating  platinum  wire  by  means  of, 
302; 

induced  by  cutting  lines  of  force,  321 ; 

magnetic  effect  of,  271 ; 

measurement  of,  by  voltameter,  312 ; 

production  of,  by  means  of  heat,  315 ; 

transformation  of  energy  by  means 
of,  302 ; 

induced  by  moving  a  wire,  321. 
Curve,  the  ballistic,  34 ; 

of  sines,  54. 

Dark-line  spectra,  386. 
Density,  defined,  122 ; 

measurement  of,  123; 

of  certain  substances,  128. 


Diamagnetism  defined,  289. 

Diameters,  law  of,  132. 

Difference  of    potential  of  a  voltaic 

cell,  265. 

Dipping  needle,  281.  ' 
Direction  of  thermo-electric  current  in 

antimony  and  bismuth,  317. 
Discharge  in  vacuo,  258,  260. 
Disruptive  discharge,  255. 
Dispersion  defined,  382. 
Distance    and    size,    estimation    of, 

416. 

Distribution  of  charge,  240. 
Diverging  lenses,  391. 
Double  refraction,  404; 

in  strained  glass,  408. 
Dynamos  and  motors,  326. 

Ebullition,  177. 
Elasticity,  95 ; 

limit  of,  96 ; 

of  torsion,  105. 
Electric  current,  the,  265. 
Electrical  machines,  225. 
Electricity,  defined,  211 ; 

hypothesis  of  two  fluids,  216 ; 

quantity  of,  237. 
Electrification,  defined,  213; 

by  chemical  action,  264. 
Electrochemical  equivalents  (table  of) , 

314. 
Electrolysis,  the  law  of,  307 ; 

of  copper,  309 ; 

of  sodium,  310. 
Electromagnets,  289. 
Electromotive  force    and    resistance, 

294. 

Electrophorus,  the,  227. 
Electroscope,  the,  214. 
Electrostatic  attraction,  211. 
Electrostatic  repulsion,  213. 
Electrostatic  series,  223. 
Energy,  conservation  of,  65 ; 

heat  a  form  of,  161; 

kinetic,  58 ; 

of  pendulum,  61 ; 

of  the  spark,  256 ; 

potential,  58; 

transformation  of,  by  electric  cur- 
rent, 302. 


INDEX 


447 


Equilibrium,  conditions  of,  75 ; 

stable  and  unstable,  75. 
Equivalents,  electrochemical,  314. 
Erg,  the,  60. 
Estimation  of  tenths,  6. 
Evaporation,  freezing  by,  179; 

influence  of,  upon  temperature,  184. 
Expansion  of  a  bar,  148 ; 

of  gases,  151 ; 

of  liquids,  149; 

of  liquids  (absolute) ,  150. 
Extraordinary  ray,  the,  405. 
Eye,  the,  413. 
Eyepieces,  393. 

Fall  of  potential,  293. 
Falling  bodies,  laws  of,  19. 
Faraday's  bag,  236 ; 

ice-pail  experiment,  235. 
Far  and  near  sightedness,  414. 
Field,  the  magnetic,  271 ; 

magnetic,  of  the  earth,  280 ; 

of  a  coil,  influence  of  iron  upon,  287. 
Figures,  of  Lissajous,  354. 
Fire  syringe,  the,  190. 
Flame,  the  sensitive,  334. 
Fluids,  hypothesis  of  two,  216. 
Focal  length  of  a  lens,  391. 
Focal  length  of  lens  and  size  of  image, 

395. 
Foci,  conjugate,  374; 

of  a  lens,  391. 
Focus,  the  principal,  374. 
Foot  pound,  the,  61. 
Force,  definition  of,  10 ; 

moment  of  a,  defined,  67. 
Forces,  cohesive,  88 ; 

composition  of,  11 ; 

graphical  representation  of,  11 ; 

in  equilibrium,  75; 

molecular,  86 ; 

parallelogram  of,  12 ; 

polygon  of,  13. 
Fraunhofer  lines,  387. 
Friction,  86; 

electrical  charging,  by,  222 ; 

sliding,  89 ; 

starting,  92 ; 

of  a  shaft,  94 ; 

rolling,  94. 


Fulcrum,  the,  67. 
Fundamental  tones,  347 ; 

tone  of  a  pipe,  366. 
Fusion,  change  of  volume  due  to,  174 ; 

heat  of,  169. 

alileo's  experiments,  19. 
alvanometer,  the,  291. 
Galvanometer  needles,  forms  of,  292. 
alvanometers,  sensitive,  292. 
as,  definition  of,  137 ; 

measurement  of  mass  of,  137. 
Gases,  expansion  of,  151 ; 
Pascal's  principle  for,  139 ; 
properties  of,  137 ; 
specific  heat  of,  165. 
ay-Lussac's  law,  150. 
Geissler  tubes,  262. 
Glass,  conducting  power  of,  194. 
Glow  lamps,  303 ; 

determination  of  power  expended 

upon,  304. 
Graduation  of  a  thermometer,  153. 
Grain,  the,  defined,  3. 
Gram  and  grain  compared,  4. 
Gravitation,  21 ; 

in  combination  with  other  forces,  31 ; 
measurements  of,  55. 

Hare's  method,  127. 
Heat,  defined,  W8;  -'  I 

a  form  of  energy,  161 ; 

and  work,  relations  between,  187 ; 

capacity  for,  161 ; 

mechanical  equivalent  of,  187,  192 ; 

nature  and  effects  of,  148 ; 

of  friction,  steam  from,  188; 

of  fusion,  169; 

of  fusion,  numerical  values  of,  170 ; 

of  vaporization,  171 ; 

production  of  current  by  means  of, 
315; 

specific,  163 ; 

specific,  of  a  metal,  164; 

transmission  of,  194 ; 

transmission  by  radiation,  204; 

units,  163. 

Holmgren  test  for  color  blindness,  424. 
Holtz  machines,  233. 
Humors  of  the  eye,  415. 


448 


INDEX 


Hydraulic  press,  110. 
Hydrometer,  method  of,  124 ; 

Nicholson's,  125. 
Hydrometers  of  constant  immersion, 

125. 
Hydrostatic  pressure,  108. 

Ice-block  calorimeter,  the,  165. 
Ice-pail  experiment,  235. 
Image  in  plane  mirror,  372. 
Images,  formed  by  lenses,  391; 

real  and  virtual,  374. 
Incidence,  angle  of,  371. 
Inclined  plane,  72 ; 

method  of  the,  22; 

relations  of  screw  to,  73. 
Index  of  refraction,  378. 
Induced  current,  321. 
Induced  currents  by  the  starting  or 
stopping  of  currents  in  a  neigh- 
boring circuit,  329.  . 
Induction,  charging  by,  218 ; 

coils,  330 ; 

magnetization  by,  284. 
Inertia,  law  of,  14 ; 

moment  of,  62. 
Influence  machines,  229. 
Influence  of  temperature  upon  resist- 
ance, 300. 
Interference  colors  in  nature,  411 ; 

of  light,  408. 
Ions,  defined,  307. 
Iridescence,  411. 
Iris,  the,  415. 
Iron,  conducting  power  of,  194 ; 

magnetization  of,  273. 
Isochronism,  law  of,  41. 

Joule's  law,  302. 

Kilogram,  the  standard,  3; 

and  pound  compared,  4. 
Kilometer  and  mile  compared,  4. 
Kinetic  energy,  58 ; 

measured,  60. 
Kirehhoff's  law,  207. 

Lamp,  the  glow  or  incandescent,  303. 
Law,  Boyle's,  137 ; 
Charles's,  157. 


Law,  Gay-Lussac's,  158; 

Joule's,  302 ; 

Kirehhoff's,  207 ; 

Mariotte's,  137 ; 

Ohm's,  294 ; 

of  the  conservation  of  energy,  64 ; 

of  diameters,  132 ; 

of  electrolysis,  307 ; 

of  inertia,  14 ; 

of  isochronism,  41 ; 

of  the  lever,  68 ; 

of  the  simple  pendulum,  38; 

of  the  simple  pendulum,  formula 

of,  45. 
Laws  of  falling  bodies,  19 ; 

of  friction,  90; 

of  motion,  10, 13,  23. 
Leakage,  measurement  of,  145. 
Length,  measurements  of,  1 ; 

units  of,  2. 
Lenses,  defined,  390 ; 

converging  and  diverging,  391. 
Leslie's  cube,  206. 
Lever,  the,  defined,  66 ; 

law  of  the,  68 ; 

principle  of  work  applied  to,  70. 
Leyden  jar,  the,  245. 
Light,  the  arc,  305; 

composition  of,  382 ; 

propagation  of,  370 ; 

reflection  of,  371 ; 

velocity  of,  370. 
Limits  of  audibility,  342. 
Lines  of  Fraunhofer,  387. 
Liquid,  convection  currents  in,  198. 
Liquids,  conductivity  of,  196; 

density  of,  127 ; 

expansion  of,  149 ; 

properties  of,  108 ; 

properties  of  surface  films  of,  130 ; 

specific  heat  of,  165. 
Lissajous's  figures,  354 ; 

method,  353. 
Liter  and  quart  compared,  4. 

Machine,  definition  of  a,  65 ; 

the  Holtz,  233 ; 

the  Toepler-Holtz,  230 ; 

the  Wimshurst,  233. 
Machines,  electrical,  225. 


INDEX 


449 


Machines,  influence,  229 ; 

simple,  65. 

Magnet,  action  of  current  upon  a,  277. 
Magnetic  effects  of  the  current,  271. 
Magnetic  field,  the,  271; 

of  the  earth,  280 ; 

of  a  coil  of  wire,  272. 
Magnetic  pole,  nature  of,  281. 
Magnetic  saturation,  288. 
Magnetization,  by  induction,  284  ; 

by  the  earth's  field,  285 ; 

of  chromium,  289 ; 

of  iron  by  means  of  a  solenoid,  273 ; 

of  manganese,  289 ; 

of  nickel,  289 ; 

of  steel,  275. 
Magnifying  power,  396. 
Manometers,  143. 
Manometric  flame,  the,  368 ; 

analysis  of  sound  by,  368. 
Mariotte's  law,  137. 
Mass,  measurement  of,  1 ; 

unit  of,  3. 

Measurement  of  resistance  by  Wheat- 
stone's  bridge,  299. 
Measurements,  physical,  1; 

of  length,  6. 
Melting  point,  influence  of  pressure 

on,  176. 

Menzel  and  Raps's  experiment,  358. 
Metals,  resistance  of,  296. 
Meter,  the,  2 ; 

and  inch  compared,  4. 
Method  of  mixtures,  163. 
Metric  system,  1 ; 

units  of,  3. 
Metronome,  the,  5 ; 

illustrations  of,  application  of,  5 ; 

testing  of,  46. 
Micrometer,  the  eyepiece,  401 ; 

the  stage,  401. 
Microscope,  the,  400. 
Mirrors,  convex  and  concave,  373 ; 

plane,  372. 

Mixtures,  method  of,  163. 
Modulus,  Young's,  etc.,  100. 
Molecular  forces,  86. 
Motion,  characteristics  of,  10 ; 

energy  of,  59 ; 

laws  of,  10,  13. 


Motion,  of  pendulum,  analysis  of,  53; 

simple  harmonic,  53 ; 

uniform,  defined,  10. 
Motors  and  dynamos,  326. 
Musical,  instrument,  parts  of  a,  365. 

tones  and  noises,  343. 

Near  and  far  sightedness,  414. 
Needle,  dipping,  281. 
Neutral  point,  the,  319. 
Newton's  laws  of  motion,  13; 

rings,  411. 

Nicholson  hydrometer,  the,  125. 
Nicol  prism,  the,  405. 
Nodal  lines,  344. 

Nodes,  in^a  vibrating  string,  356. 
Noises,  defined,  343. 

Object  lens  of  telescopes,  394. 

Ohm's  law,  294. 

Open  and  closed  pipes,  362. 

Optical  study  of  vibration,  353. 

Ordinary  ray,  the,  405. 

Organ  pipe,  the,  365. 

Organ  pipes,  open  and  closed,  362. 

Oscillation,  to  find  center  of,  51. 

Overtones,  347 ; 

of  wind  instruments,  367. 

Parallelogram  of  forces,  12. 

Pascal's  principle  applied  to  gases,  159 ; 

vases,  114. 

Peltier  effect,  the,  316. 
Pendulum,  definition  of,  terms  refer- 
ring to,  38 ; 

analysis  of  the  motion  of,  53 ; 

energy  of,  61 ; 

isochronism  of,  41 ; 

law  of,  38; 

law  of  equal  times,  41 ; 

law  of  relation  between  force  and 
period,  44 ; 

the  physical,  53 ; 

the  reversion,  56 ; 

the  simple,  37 ; 

which  beats  seconds,  length  of,  47. 
Permeability,  bodies  of  low,  290. 
Phenomena    accompanying  vaporiza- 
tion, 177. 
Physical  measurements,  161. 


450 


INDEX 


Physical  pendulum,  51. 
Physics,  denned,  11; 

branches  of,  1. 
Pipes,  closed  and  open,  362. 
Pitch,  defined,  342; 

influence  of  temperature  on,  367; 

of  a  pipe,  366 ; 

of  a  pipe,  modified  by  the  contained 
gas,  367 ; 

of  vibrating  strings,  SCO ; 

relative  and  absolute,  351. 
Plane,  the  inclined,  72. 
Plates,  vibrating,  341. 
Plunge  battery,  the,  270. 
Points,  action  of,  241. 
Polarization,  by  double  refraction,  404 ; 

by  reflection,  403; 

of  the  voltaic  cell,  268. 
Polarized  light,  403. 
Polarizer  and  analyzer,  406. 
Poles,  magnetic,  281. 
Polygon  of  forces,  the,  13. 
Potassium    permanganate,    spectrum 

of,  388. 
Potential,  difference  of,  265; 

energy,  58 ; 

energy  of  configuration,  60; 

fall  of,  293. 

Press,  the  hydraulic,  110. 
Pressure,  distribution  of,  112; 

gauges,  144; 

hydrostatic,  108 ; 

influence    of,    upon    the    electric 
:       spark,  257; 

influence  of,  on  the  melting  point, 
176; 

relation  between  boiling  point  and, 
180; 

transmission  of,  109. 
Principal  focus  of  a  mirror,  374 ; 

of  a  lens,  391. 

Principle  of  Archimedes,  116,  122. 
Prism,  passage  of  light  through  a,  379. 
Production  of  current  by  heat,  315. 
Projectiles,  defined,  31. 
Propagation  of  light,  370. 
Properties  of  gases,  137; 

of  liquids,  108. 
Pulley,  the,  defined,  65; 

considered  as  a  lever,  70. 


Pure  spectrum,  formation  of  a,  384. 
Purity  of  color,  418. 

Quadrant  electrometer,  the,  252. 
Quantity,  of  electricity,  237. 

Radiation,  194,  202 ; 

and  temperature,  210; 

influence  of  surface  upon,  206. 
Raps  and  MenzePs  experiment,  360. 
Reaction,  illustration  of,  16. 
Real  images,  374. 
Reflecting  telescopes,  377. 
Reflection,  angle  of,  371; 

of  sound,  340; 

the  law  of,  371; 

total,  380. 
Refracting  telescopes,  393. 
Refraction,  angle  of,  378 ; 

double,  404 ; 

index  of,  378 ; 

law  of,  377. 
Relative  pitch,  351. 
Repulsion,  electrostatic,  213. 
Resistance,  boxes,  298 ; 

and  electromotive  force,  294; 

influence  of  temperature  upon,  300; 

measurement  of,  299 ; 

specific,  296. 
Resolution  of  forces,  11. 
Resonance  of  an  air  column,  363. 
Resonators,  364. 
Retina,  the,  413. 
Reversal  of  sodium  lines,  386. 
Rods,  torsion  of,  106 ; 

vibrating,  341. 
Roentgen  rays,  262. 
Rosse,  the  great  telescope  of,  377. 

Saturation,  magnetic,  288; 

of  color,  418. 
Segments,  vibrating,  344. 
Sensitive  flame,  the,  334. 
Sensitive  galvanometers,  292. 
Silver  voltameter,  the,  313. 
Simple  cell,  the,  266. 
Sines,  curve  of,  54. 
Size  of   image  and  focal   length   of 

lens,  395. 
Size  and  distance,  estimation  of,  416. 


450 

Physi 

Physi 

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Pipes 

Pitch 

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Plate 

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Pola: 

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Pola 
Pola 
Pole; 
Poly 
Pota 

Pote 

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Pres 

Pres 

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Pri 
Prii 
Prc 
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